Results for 'Clifford algebra'

971 found
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  1. Clifford Algebras and the Dirac-Bohm Quantum Hamilton-Jacobi Equation.B. J. Hiley & R. E. Callaghan - 2012 - Foundations of Physics 42 (1):192-208.
    In this paper we show how the dynamics of the Schrödinger, Pauli and Dirac particles can be described in a hierarchy of Clifford algebras, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}${\mathcal{C}}_{1,3}, {\mathcal{C}}_{3,0}$\end{document}, and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}${\mathcal{C}}_{0,1}$\end{document}. Information normally carried by the wave function is encoded in elements of a minimal left ideal, so that all the physical information appears within the algebra itself. The state of the quantum process (...)
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  2. Clifford Algebras in Symplectic Geometry and Quantum Mechanics.Ernst Binz, Maurice A. de Gosson & Basil J. Hiley - 2013 - Foundations of Physics 43 (4):424-439.
    The necessary appearance of Clifford algebras in the quantum description of fermions has prompted us to re-examine the fundamental role played by the quaternion Clifford algebra, C 0,2 . This algebra is essentially the geometric algebra describing the rotational properties of space. Hidden within this algebra are symplectic structures with Heisenberg algebras at their core. This algebra also enables us to define a Poisson algebra of all homogeneous quadratic polynomials on a two-dimensional (...)
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  3.  74
    Clifford algebras and Hestenes spinors.Pertti Lounesto - 1993 - Foundations of Physics 23 (9):1203-1237.
    This article reviews Hestenes' work on the Dirac theory, where his main achievement is a real formulation of the theory within thereal Clifford algebra Cl 1,3 ≃ M2 (H). Hestenes invented first in 1966 hisideal spinors $\phi \in Cl_{1,3 _2}^1 (1 - \gamma _{03} )$ and later 1967/75 he recognized the importance of hisoperator spinors ψ ∈ Cl 1,3 + ≃ M2 (C).This article starts from the conventional Dirac equation as presented with matrices by Bjorken-Drell. Explicit mappings are (...)
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  4.  65
    Clifford Algebra Formulation of an Electromagnetic Charge-Current Wave Theory.Amr M. Shaarawi - 2000 - Foundations of Physics 30 (11):1911-1941.
    In this work, a Clifford algebra approach is used to introduce a charge-current wave structure governed by a Maxwell-like set of equations. A known spinor representation of the electromagnetic field intensities is utilized to recast the equations governing the charge-current densities in a Dirac-like spinor form. Energy-momentum considerations lead to a generalization of the Maxwell electromagnetic symmetric energy-momentum tensor. The generalized tensor includes new terms that represent contributions from the charge-current densities. Stationary spherical modal solutions representing the charge-current (...)
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  5. Clifford-Algebra Based Polydimensional Relativity and Relativistic Dynamics.Matej Pavšič - 2001 - Foundations of Physics 31 (8):1185-1209.
    Starting from the geometric calculus based on Clifford algebra, the idea that physical quantities are Clifford aggregates (“polyvectors”) is explored. A generalized point particle action (“polyvector action”) is proposed. It is shown that the polyvector action, because of the presence of a scalar (more precisely a pseudoscalar) variable, can be reduced to the well known, unconstrained, Stueckelberg action which involves an invariant evolution parameter. It is pointed out that, starting from a different direction, DeWitt and Rovelli postulated (...)
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  6.  45
    Clifford Algebraic Computational Fluid Dynamics: A New Class of Experiments.William Kallfelz - unknown
    Though some influentially critical objections have been raised during the ‘classical’ pre-computational simulation philosophy of science tradition, suggesting a more nuanced methodological category for experiments, it safe to say such critical objections have greatly proliferated in philosophical studies dedicated to the role played by computational simulations in science. For instance, Eric Winsberg suggests that computer simulations are methodologically unique in the development of a theory’s models suggesting new epistemic notions of application. This is also echoed in Jeffrey Ramsey’s notions of (...)
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  7.  40
    Galilean-Covariant Clifford Algebras in the Phase-Space Representation.J. D. M. Vianna, M. C. B. Fernandes & A. E. Santana - 2005 - Foundations of Physics 35 (1):109-129.
    We apply the Galilean covariant formulation of quantum dynamics to derive the phase-space representation of the Pauli–Schrödinger equation for the density matrix of spin-1/2 particles in the presence of an electromagnetic field. The Liouville operator for the particle with spin follows from using the Wigner–Moyal transformation and a suitable Clifford algebra constructed on the phase space of a (4 + 1)-dimensional space–time with Galilean geometry. Connections with the algebraic formalism of thermofield dynamics are also investigated.
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  8.  64
    Octonionic representations of Clifford algebras and triality.Jörg Schray & Corinne A. Manogue - 1996 - Foundations of Physics 26 (1):17-70.
    The theory of representations of Clifford algebras is extended to employ the division algebra of the octonions or Cayley numbers. In particular, questions that arise from the nonassociativity and noncommutativity of this division algebra are answered. Octonionic representations for Clifford algebras lead to a notion of octonionic spinors and are used to give octoninic representations of the respective orthogonal groups. Finally, the triality automorphisms are shown to exhibit a manifest Σ 3 ×SO(8) structure in this framework.
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  9.  69
    A unifying Clifford algebra formalism for relativistic fields.K. R. Greider - 1984 - Foundations of Physics 14 (6):467-506.
    It is shown that a Clifford algebra formalism provides a unifying description of spin-0, -1/2, and-1 fields. Since the operators and operands are both expressed in terms of the same Clifford algebra, the formalism obtains some results which are considerably different from those of the standard formalisms for these fields. In particular, the conservation laws are obtained uniquely and unambiguously from the equations of motion in this formalism and do not suffer from the ambiguities and inconsistencies (...)
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  10. 2nd workshop on Clifford algebras and their applications in mathematical physics.Dm Greenberger - 1991 - Foundations of Physics 21 (6):735-752.
     
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  11.  20
    The common sense of the exact sciences.William Kingdon Clifford, Karl Pearson & Richard Charles Rowe - 1946 - New York,: A.A. Knopf. Edited by Karl Pearson & James R. Newman.
    "Clifford was famous for his public lectures on physics and math and ethics because he explained complex things with easily understood, concrete examples. As you read through his clear, simple explanations of the true bases of number, algebra and geometry you will find yourself getting angry and saying "Why the hell wasn't I taught math this way?" and "Do math ed professors know so little mathematics that they have never heard of Clifford.?" Clifford was destined to (...)
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  12.  83
    SO(m)-invariant differential operators on Clifford algebra-valued functions.F. Sommen & N. Van Acker - 1993 - Foundations of Physics 23 (11):1491-1519.
    In this paper we consider the algebra of differential operators with polynomial coefficients acting on Clifford algebra-valued functions from both sides. We characterize the subalgebra of SO(m)-invariant differential operators, which itself contains the subalgebra of GL(m)-invariant differential operators.
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  13.  19
    The common sense of the exact sciences.William Kingdon Clifford, James Roy Newman & Karl Pearson - 1946 - New York,: A.A. Knopf. Edited by Karl Pearson & James R. Newman.
    "Clifford was famous for his public lectures on physics and math and ethics because he explained complex things with easily understood, concrete examples. As you read through his clear, simple explanations of the true bases of number, algebra and geometry you will find yourself getting angry and saying "Why the hell wasn't I taught math this way?" and "Do math ed professors know so little mathematics that they have never heard of Clifford.?" Clifford was destined to (...)
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  14. Book review: Clifford algebra: A computational tool for physicists, by John snygg. [REVIEW]Pertti Lounesto - 1998 - Foundations of Physics 28 (6):1021-1021.
  15.  74
    Pauli-Dirac matrix generators of Clifford Algebras.Charles P. Poole & Horacio A. Farach - 1982 - Foundations of Physics 12 (7):719-738.
    This article presents a Pauli-Dirac matrix approach to Clifford Algebras. It is shown that the algebra C2 is generated by two Pauli matrices iσ2 and iσ3; C3 is generated by the three Pauli matrices σ1, σ2, σ3; C4 is generated by four Dirac matrices γ0, γ1, γ2, γ3 and C5 is generated by five Dirac matrices iγ0, iγ1, iγ2, iγ3, iγ5. The higher dimensional anticommuting matrices which generate arbitrarily high order Clifford algebras are given in closed form. (...)
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  16.  63
    Embedding fundamental aspects of the relational blockworld interpretation in geometric (or clifford) algebra.William Kallfelz - unknown
    I summarize Silberstein, et. al’s (2006) discussion of the derivation of the Heisenberg commutators, whose work is based on Kaiser (1981, 1990) and Bohr, et. al. (1995, 2004a,b). I argue that Bohr and Kaiser’s treatment is not geometric enough, as it still relies on some unexplained residual notions concerning the unitary representation of transformations in a Hilbert space. This calls for a more consistent characterization of the role of i than standard QM can offer. I summarize David Hestenes’ (1985,1986) major (...)
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  17.  48
    On invertibility in high-dimensional Clifford algebras.Pavel Semenov - 1993 - Foundations of Physics 23 (11):1543-1546.
  18. On Clifford representation of Hopf algebras and fierz identities.Suemi Rodríguez-Romo - 1996 - Foundations of Physics 26 (11):1457-1468.
    We present a short review of the action and coaction of Hopf algebras on Clifford algebras as an introduction to physically meaningful examples. Some q-deformed Clifford algebras are studied from this context and conclusions are derived.
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  19.  44
    The Charge–Mass–Spin Relation of Clifford Polyparticles, Kerr–Newman Black Holes and the Fine Structure Constant.Carlos Castro - 2004 - Foundations of Physics 34 (7):1091-1113.
    A Clifford-algebraic interpretation is proposed of the charge, mass, spin relationship found recently by Cooperstock and Faraoini, which was based on the Kerr–Newman metric solutions of the Einstein–Maxwell equations. The components of the polymomentum associated with a Clifford polyparticle in four dimensions provide for such a charge, mass, spin relationship without the problems encountered in Kaluza–Klein compactifications which furnish an unphysically large value for the electron charge. A physical reasoning behind such charge, mass, spin relationship is provided, followed (...)
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  20.  98
    Clifford Space as the Arena for Physics.Matej Pavšsič - 2003 - Foundations of Physics 33 (9):1277-1306.
    A new theory is considered according to which extended objects in n-dimensional space are described in terms of multivector coordinates which are interpreted as generalizing the concept of center of mass coordinates. While the usual center of mass is a point, by generalizing the latter concept, we associate with every extended object a set of r-loops, r=0,1,...,n−1, enclosing oriented (r+1)-dimensional surfaces represented by Clifford numbers called (r+1)-vectors or multivectors. Superpositions of multivectors are called polyvectors or Clifford aggregates and (...)
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  21.  70
    On Clifford Space Relativity, Black Hole Entropy, Rainbow Metrics, Generalized Dispersion and Uncertainty Relations.Carlos Castro - 2014 - Foundations of Physics 44 (9):990-1008.
    An analysis of some of the applications of Clifford space relativity to the physics behind the modified black hole entropy-area relations, rainbow metrics, generalized dispersion and minimal length stringy uncertainty relations is presented.
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  22.  66
    The algebraization of quantum mechanics and the implicate order.F. A. M. Frescura & B. J. Hiley - 1980 - Foundations of Physics 10 (9-10):705-722.
    It has been proposed that the implicate order can be given mathematical expression in terms of an algebra and that this algebra is similar to that used in quantum theory. In this paper we bring out in a simple way those aspects of the algebraic formulation of quantum theory that are most relevant to the implicate order. By using the properties of the standard ket introduced by Dirac we describe in detail how the Heisenberg algebra can be (...)
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  23.  52
    Algebraic field descriptions in three-dimensional Euclidean space.Nikos Salingaros & Yehiel Ilamed - 1984 - Foundations of Physics 14 (8):777-797.
    In this paper, we use the differential forms of three-dimensional Euclidean space to realize a Clifford algebra which is isomorphic to the algebra of the Pauli matrices or the complex quaternions. This is an associative vector-antisymmetric tensor algebra with division: We provide the algebraic inverse of an eight-component spinor field which is the sum of a scalar + vector + pseudovector + pseudoscalar. A surface of singularities is defined naturally by the inverse of an eight-component spinor (...)
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  24.  71
    Clifford Space as a Generalization of Spacetime: Prospects for QFT of Point Particles and Strings. [REVIEW]Matej Pavšič - 2005 - Foundations of Physics 35 (9):1617-1642.
    The idea that spacetime has to be replaced by Clifford space (C-space) is explored. Quantum field theory (QFT) and string theory are generalized to C-space. It is shown how one can solve the cosmological constant problem and formulate string theory without central terms in the Virasoro algebra by exploiting the peculiar pseudo-Euclidean signature of C-space and the Jackiw definition of the vacuum state. As an introduction into the subject, a toy model of the harmonic oscillator in pseudo-Euclidean space (...)
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  25.  44
    On Endomorphisms of Ockham Algebras with Pseudocomplementation.T. S. Blyth & J. Fang - 2011 - Studia Logica 98 (1-2):237-250.
    A pO -algebra $${(L; f, \, ^{\star})}$$ is an algebra in which ( L ; f ) is an Ockham algebra, $${(L; \, ^{\star})}$$ is a p -algebra, and the unary operations f and $${^{\star}}$$ commute. Here we consider the endomorphism monoid of such an algebra. If $${(L; f, \, ^{\star})}$$ is a subdirectly irreducible pK 1,1 - algebra then every endomorphism $${\vartheta}$$ is a monomorphism or $${\vartheta^3 = \vartheta}$$ . When L is finite (...)
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  26.  44
    Some remarks on the algebra of Eddington'sE numbers.Nikos Salingaros - 1985 - Foundations of Physics 15 (6):683-691.
    This paper reviews the algebra of Eddington'sE numbers and identifies those points where Eddington anticipated results of current interest. He discovered the Majorana spinors, and was responsible for the standard γ 5 notation as well as the notion of chirality. Furthermore, Eddington defined Clifford algebras in eight and nine dimensions which are now appearing in grand unified gauge and supersymmetric theories. A point which Eddington cleared up, yet is still misunderstood, is that the Dirac algebra corresponds to (...)
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  27.  71
    Flat algebras and the translation of universal Horn logic to equational logic.Marcel Jackson - 2008 - Journal of Symbolic Logic 73 (1):90-128.
    We describe which subdirectly irreducible flat algebras arise in the variety generated by an arbitrary class of flat algebras with absorbing bottom element. This is used to give an elementary translation of the universal Horn logic of algebras, and more generally still, partial structures into the equational logic of conventional algebras. A number of examples and corollaries follow. For example, the problem of deciding which finite algebras of some fixed type have a finite basis for their quasi-identities is shown to (...)
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  28.  42
    Distance geometry and geometric algebra.Andreas W. M. Dress & Timothy F. Havel - 1993 - Foundations of Physics 23 (10):1357-1374.
    As part of his program to unify linear algebra and geometry using the language of Clifford algebra, David Hestenes has constructed a (well-known) isomorphism between the conformal group and the orthogonal group of a space two dimensions higher, thus obtaining homogeneous coordinates for conformal geometry.(1) In this paper we show that this construction is the Clifford algebra analogue of a hyperbolic model of Euclidean geometry that has actually been known since Bolyai, Lobachevsky, and Gauss, and (...)
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  29.  41
    Real and holomorphic SuSy algebras.R. A. Marques Pereira - 1989 - Foundations of Physics 19 (6):755-782.
    We propose a new constructive scheme for real SuSy algebras within the general formalism of real Clifford algebra theory, and use it to characterize a natural holomorphic extension admitted by a subclass of real SuSy algebras in signaturess−t=3 mod 4. The resulting holomorphic SuSy algebras are the abstract models of a new type of supersymmetry algebras, already known to be relevant in the development of canonical or Hamiltonian methods in superspace.
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  30.  91
    The Extended Relativity Theory in Born-Clifford Phase Spaces with a Lower and Upper Length Scales and Clifford Group Geometric Unification.Carlos Castro - 2005 - Foundations of Physics 35 (6):971-1041.
    We construct the Extended Relativity Theory in Born-Clifford-Phase spaces with an upper R and lower length λ scales (infrared/ultraviolet cutoff). The invariance symmetry leads naturally to the real Clifford algebra Cl (2, 6, R) and complexified Clifford Cl C (4) algebra related to Twistors. A unified theory of all Noncommutative branes in Clifford-spaces is developed based on the Moyal-Yang star product deformation quantization whose deformation parameter involves the lower/upper scale $$(\hbar \lambda / R)$$. Previous (...)
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  31.  37
    On generalized electromagnetism and Dirac algebra.David Fryberger - 1989 - Foundations of Physics 19 (2):125-159.
    Using a framework of Dirac algebra, the Clifford algebra appropriate for Minkowski space-time, the formulation of classical electromagnetism including both electric and magnetic charge is explored. Employing the two-potential approach of Cabibbo and Ferrari, a Lagrangian is obtained that is dyality invariant and from which it is possible to derive by Hamilton's principle both the symmetrized Maxwell's equations and the equations of motion for both electrically and magnetically charged particles. This latter result is achieved by defining the (...)
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  32.  48
    From the Geometry of Pure Spinors with Their Division Algebras to Fermion Physics.Paolo Budinich - 2002 - Foundations of Physics 32 (9):1347-1398.
    The Cartan equations defining simple spinors (renamed “pure” by C. Chevalley) are interpreted as equations of motion in compact momentum spaces, in a constructive approach in which at each step the dimensions of spinor space are doubled while those of momentum space increased by two. The construction is possible only in the frame of the geometry of simple or pure spinors, which imposes contraint equations on spinors with more than four components, and then momentum spaces result compact, isomorphic to invariant-mass-spheres (...)
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  33.  72
    Direct product and decomposition of certain physically important algebras.Robert W. Johnson - 1996 - Foundations of Physics 26 (2):197-222.
    I consider the direct product algebra formed from two isomorphic Clifford algebras. More specifically, for an element x in each of the two component algebras I consider elements in the direct product space with the form x ⊗ x. I show how this construction can be used to model the algebraic structure of particular vector spaces with metric, to describe the relationship between wavefunction and observable in examples from quantum mechanics, and to express the relationship between the electromagnetic (...)
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  34.  75
    The implicate order, algebras, and the spinor.F. A. M. Frescura & B. J. Hiley - 1980 - Foundations of Physics 10 (1-2):7-31.
    We review some of the essential novel ideas introduced by Bohm through the implicate order and indicate how they can be given mathematical expression in terms of an algebra. We also show how some of the features that are needed in the implicate order were anticipated in the work of Grassmann, Hamilton, and Clifford. By developing these ideas further we are able to show how the spinor itself, when viewed as a geometric object within a geometric algebra, (...)
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  35.  77
    An Einstein addition law for nonparallel boosts using the geometric algebra of space-time.B. Tom King - 1995 - Foundations of Physics 25 (12):1741-1755.
    The modern use of algebra to describe geometric ideas is discussed with particular reference to the constructions of Grassmann and Hamilton and the subsequent algebras due to Clifford. An Einstein addition law for nonparallel boosts is shown to follow naturally from the use of the representation-independent form of the geometric algebra of space-time.
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  36. A Survey of Geometric Algebra and Geometric Calculus.Alan Macdonald - 2017 - Advances in Applied Clifford Algebras 27:853-891.
    The paper is an introduction to geometric algebra and geometric calculus for those with a knowledge of undergraduate mathematics. No knowledge of physics is required. The section Further Study lists many papers available on the web.
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  37.  88
    A common abstraction of MV-Algebras and Abelian l-groups.Francesco Paoli - 2000 - Studia Logica 65 (3):355-366.
    We investigate the class of strongly distributive pregroups, a common abstraction of MV-algebras and Abelian l-groups which was introduced by E.Casari. The main result of the paper is a representation theorem which yields both Chang's representation of MV-algebras and Clifford's representation of Abelian l-groups as immediate corollaries.
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  38. The emergence of a Kaluza-Klein microgenometry from the invariants of optimally Euclidean Lorentzian spaces.José G. Vargas & Douglas G. Torr - 1997 - Foundations of Physics 27 (4):533-558.
    It is shown that relativistic spacetimes can be viewed as Finslerian spaces endowed with a positive definite distance (ω0, mod ωi) rather than as pariah, pseudo-Riemannian spaces. Since the pursuit of better implementations of “Euclidicity in the small” advocates absolute parallelism, teleparallel nonlinear Euclidean (i.e., Finslerian) connections are scrutinized. The fact that (ωμ, ω0 i) is the set of horizontal fundamental 1-forms in the Finslerian fibration implies that it can be used in principle for obtainingcompatible new structures. If the connection (...)
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  39.  38
    A Hilbert space for the classical electromagnetic field.Bernard Jancewicz - 1993 - Foundations of Physics 23 (11):1405-1421.
    The synthetic Maxwell equation, uniting all Maxwell equations within the framework of a Clifford algebra, can be treated as a first-order wave equation. A Hilbert space of its solutions describing classical free electromagnetic fields is introduced. This Hilbert space can be called “classical,” which means that the Planck constant is absent. The scalar square of an element of this space is the total energy of the field. The time independence of the scalar product is demonstrated. The time and (...)
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  40.  78
    A Velocity Field and Operator for Spinning Particles in (Nonrelativistic) Quantum Mechanics.Giovanni Salesi & Erasmo Recami - 1998 - Foundations of Physics 28 (5):763-773.
    Starting from the formal expressions of the hydrodynamical (or “local”) quantities employed in the applications of Clifford algebras to quantum mechanics, we introduce—in terms of the ordinary tensorial language—a new definition for the field of a generic quantity. By translating from Clifford into tensor algebra, we also propose a new (nonrelativistic) velocity operator for a spin- ${\frac{1}{2}}$ particle. This operator appears as the sum of the ordinary part p/m describing the mean motion (the motion of the center-of-mass), (...)
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  41. Unified spin gauge model and the top quark mass.J. S. R. Chisholm & R. S. Farwell - 1995 - Foundations of Physics 25 (10):1511-1522.
    Spin gauge models use a real Clifford algebraic structure Rp,q associated with a real manifold of dimension p + q to describe the fundamental interactions of elementary particles. This review provides a comparison between those models and the standard model, indicating their similarities and differences. By contrast with the standard model, the spin gauge model based on R3,8 generates intermediate boson mass terms without the need to use the Higgs-Kibble mechanism and produces a precise prediction for the mass of (...)
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  42.  53
    Vector-valued rational forms.D. E. Roberts - 1993 - Foundations of Physics 23 (11):1521-1533.
    We define rational Hermite interpolants to vector-valued functions and show that, in the context of Clifford algebras, the numerator and denominator polynomials belong to a complex extension of the Lipschitz group. We also discuss the problem of constructing an algebraic representation for the generalized inverse of a vector, which is at the heart of the usual development of vector rational approximation.
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  43.  39
    Scalar products of spinors and an extension of Brauer-Wall groups.Pertti Lounesto - 1981 - Foundations of Physics 11 (9-10):721-740.
    The automorphism groups of scalar products of spinors are determined. Spinors are considered as elements of minimal left ideals of Clifford algebras on quadratic modules, e.g., on orthogonal spaces. Orthogonal spaces of any dimension and arbitrary signature are discussed. For example, the automorphism groups of scalar products of Pauli spinors and Dirac spinors are, respectively, isomorphic to the matrix groups U(2) and U(2, 2). It is found that there are, in general, 32 different types or similarity classes of such (...)
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  44.  99
    On the Generalized Phase Space Approach to Duffin-Kemmer-Petiau Particles.M. C. B. Fernandes & J. D. M. Vianna - 1999 - Foundations of Physics 29 (2):201-219.
    We present a general derivation of the Duffin-Kemmer-Petiau (D.K.P) equation on the relativistic phase space proposed by Bohm and Hiley. We consider geometric algebras and the idea of algebraic spinors due to Riesz and Cartan. The generators βμ (p) of the D.K.P algebras are constructed in the standard fashion used to construct Clifford algebras out of bilinear forms. Free D.K.P particles and D.K.P particles in a prescribed external electromagnetic field are analized and general Liouville type equations for these cases (...)
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  45. Being, Becoming and the Undivided Universe: A Dialogue Between Relational Blockworld and the Implicate Order Concerning the Unification of Relativity and Quantum Theory.Michael Silberstein, W. M. Stuckey & Timothy McDevitt - 2013 - Foundations of Physics 43 (4):502-532.
    In this paper two different approaches to unification will be compared, Relational Blockworld (RBW) and Hiley’s implicate order. Both approaches are monistic in that they attempt to derive matter and spacetime geometry ‘at once’ in an interdependent and background independent fashion from something underneath both quantum theory and relativity. Hiley’s monism resides in the implicate order via Clifford algebras and is based on process as fundamental while RBW’s monism resides in spacetimematter via path integrals over graphs whereby space, time (...)
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  46. The Proof That the Standard Transformations of E and B Are Not the Lorentz Transformations.Tomislav Ivezić - 2003 - Foundations of Physics 33 (9):1339-1347.
    In this paper it is exactly proved that the standard transformations of the three-dimensional (3D) vectors of the electric and magnetic fields E and B are not relativistically correct transformations. Thence the 3D vectors E and B are not well-defined quantities in the 4D space-time and, contrary to the general belief, the usual Maxwell equations with the 3D E and B are not in agreement with the special relativity. The 4-vectors E a and B a , as well-defined 4D quantities, (...)
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  47.  63
    On a Unified Theory of Generalized Branes Coupled to Gauge Fields, Including the Gravitational and Kalb–Ramond Fields.M. Pavšič - 2007 - Foundations of Physics 37 (8):1197-1242.
    We investigate a theory in which fundamental objects are branes described in terms of higher grade coordinates $X^{\mu{_1}\ldots \mu{_n}}$ encoding both the motion of a brane as a whole, and its volume evolution. We thus formulate a dynamics which generalizes the dynamics of the usual branes. Geometrically, coordinates $X^{\mu{_1} \ldots \mu{_n}}$ and associated coordinate frame fields { ${\gamma_{\mu{_1}\ldots\mu{_n}}}$ } extend the notion of geometry from spacetime to that of an enlarged space, called Clifford space or C-space. If we start (...)
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  48.  36
    Geometrization of the physics with teleparallelism. II. Towards a fully geometric Dirac equation.José G. Vargas, Douglas G. Torr & Alvaro Lecompte - 1992 - Foundations of Physics 22 (4):527-547.
    In an accompanying paper (I), it is shown that the basic equations of the theory of Lorentzian connections with teleparallelism (TP) acquire standard forms of physical field equations upon removal of the constraints represented by the Bianchi identities. A classical physical theory results that supersedes general relativity and Maxwell-Lorentz electrodynamics if the connection is viewed as Finslerian. The theory also encompasses a short-range, strong, classical interaction. It has, however, an open end, since the source side of the torsion field equation (...)
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  49.  47
    The equations of Dirac and theM 2(ℍ)-representation ofCl 1,3.P. G. Vroegindeweij - 1993 - Foundations of Physics 23 (11):1445-1463.
    In its original form Dirac's equations have been expressed by use of the γ-matrices γμ, μ=0, 1, 2, 3. They are elements of the matrix algebra M 4 (ℂ). As emphasized by Hestenes several times, the γ-matrices are merely a (faithful) matrix representation of an orthonormal basis of the orthogonal spaceℝ 1,3, generating the real Clifford algebra Cl 1,3 . This orthonormal basis is also denoted by γμ, μ=0, 1, 2, 3. The use of the matrix (...) M 4 (ℂ) to represent Cl 1,3 has some unsatisfactory aspects. The γ-matrices contain imaginary numbers as entries whereas Cl 1,3 is real. Moreover, as a matrix algebra Cl 1,3 is M 2 (ℍ) but only a part of M 4 (ℂ). For that reason we investigate in this paper several forms of Dirac's equations in terms of M 2 (ℍ) instead of M 4 (ℂ). In Section1 we survey Dirac's equations describing the interaction of matter with electromagnetic, electroweak, and strong fields. Section2 deals with electromagnetic/weak interactions employing M 2 (ℍ). Finally, in Section3 we deal with Dirac's equations for strong interactions between quarks. In contrast to su(2) ⊕ u(1), the Lie algebra su(3) is not isomorphic to any subalgebra of Cl 1,3 . Therefore we do not give a description of strong interactions by use of M 2 (ℍ). Instead of such an approach we describe these interactions using the space of quadruples of bivector fields in Cl 1,3 . The thus obtained description has remarkable formal resemblance to the original Dirac equations using wave functions with values in the linear spaceℂ 4. (shrink)
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  50.  71
    Duality in Off-Shell Electromagnetism.Martin Land - 2005 - Foundations of Physics 35 (7):1245-1262.
    In this paper, we examine the Dirac monopole in the framework of Off-Shell Electromagnetism, the five-dimensional U(1) gauge theory associated with Stueckelberg–Schrodinger relativistic quantum theory. After reviewing the Dirac model in four dimensions, we show that the structure of the five-dimensional theory prevents a natural generaliza tion of the Dirac monopole, since the theory is not symmetric under duality transforma tions. It is shown that the duality symmetry can be restored by generalizing the electromagnetic field strength to an element of (...)
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