The classical problem of the charge and pole motion. A satisfactory formalism by Clifford algebras

Rodrigues, Waldyr A.; Recami, Erasmo; Maia, Adolfo; Rosa, M. A. F.

doi:10.1016/0370-2693(89)90036-1

Cited by 16 publications

(2 citation statements)

References 11 publications

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“…By the introduction of two potentials, Cabibbo and Ferrari have first formulated Dirac monopole theory in a manifestly covariant and symmetrical way in 1962 [66]. Similarly, an algebraic derivation of Dirac's quantization condition [67] and the first use of two potentials in a Clifford algebra approach to describe generalized electrodynamics were given by Rodrigues, Rosa, Maia and Recami [68,69].…”

Section: Generalized Electromagnetismmentioning

confidence: 99%

Hyperbolic Quaternion Formulation of Electromagnetism

Demi̇r

Tanışlı

Candemir

2010

Adv. Appl. Clifford Algebras

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In this paper, after presenting the hyperbolic quaternion formalism, an alternative representational method is proposed for the formulation of classical and generalized electromagnetism in the case of the existence of magnetic monopoles and massive photons. Maxwell's equations and relevant field equations are derived in compact, simpler and elegant forms. These equations are compared with their vectorial, complex quaternionic, dual quaternionic and octonionic representations. Mathematics Subject Classification (2000). 00A79, 8A25, 17D99.

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Section: Generalized Electromagnetismmentioning

confidence: 99%

Hyperbolic Quaternion Formulation of Electromagnetism

Demi̇r

Tanışlı

Candemir

2010

Adv. Appl. Clifford Algebras

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“…A different approach to this problem of the Lorentz force equations can be found in Ref. [21] where the Lagrangian is modified so that it becomes possible the derive the covariant form of the energy-momentum tensor directly from the La-grangian. Then, since the Lorentz equations imply the form of the energy-momentum tensor and visa versa, it is possible to obtain the Lorentz equations by taking the four-divergence of the energy-momentum tensor obtained from the modified Lagrangian.…”

Section: Discussionmentioning

confidence: 99%

Electromagnetism with magnetic charge and two photons

Singleton

1996

American Journal of Physics

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The Dirac approach to include magnetic charge in Maxwell's equations places the magnetic charge at the end of a string on which the the fields of the theory develop a singularity. In this paper an alternative formulation of classical electromagnetism with magnetic and electric charge is given by introducing a second pseudo four-vector potential, C µ , in addition to the usual fourvector potential, A µ . This avoids the use of singular, non-local variables (i.e. Dirac strings) in electrodynamics with magnetic charge, and it makes the treatment of electric and magentic charge more symmetric, since both charges are now gauge charges.

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Hydrodynamical Reformulation and Quantum Limit of the Barut-Zanghi Theory

Salesi

Recami

1998

Causality and Locality in Modern Physics

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One of the most satisfactory pictures for spinning particles is the Barut-Zanghi (BZ) classical theory for the relativistic extended-like electron, that relates spin to zitterbewegung (zbw). The BZ motion 1 equations constituted the starting point for recent works about spin and electron structure, co-authored by us, which adopted the Clifford algebra language. This language results to be actually suited for a hydrodynamical reformulation of the BZ theory. Working out a "probabilistic fluid," we are allowed to reinterpret the original classical spinors as quantum wave-functions for the electron. We can pass to "quantize" the BZ theory: by employing this time the tensorial language, more popular in first-quantization. "Quantizing" the BZ theory, however, does not lead to the Dirac equation, but rather to a nonlinear, Diraclike equation, which can be regarded as the actual "quantum limit" of the BZ classical theory. Moreover, a new variational approach to the BZ probabilistic fluid shows that it is a typical "Weyssenhoff fluid," while the Hamilton-Jacobi equation (linking mass, spin and zbw frequency together) appears to be nothing but a special case of the de So, a zbw is to be added to the usual drift, translational, or "external,"motion of the CM with velocity p/ε (which is the only one present in the case of scalar particles). In the Barut-Zanghi (BZ) theory [8,9], the classical electron was actually characterized, besides by the usual pair of conjugate variables (x µ , p µ ), by a second pair of conjugate classical spinorial variables (ψ, ψ), representing internal degrees of freedom, which are functions of the (proper) time τ measured in the electron CMF; the CMF being the one -let us remind-in which p = 0 at any instant of time. Barut and Zanghi introduced, namely, a classical Lagrangian which in the free case (i.e., when the external electromagneticwhere λ has the dimension of an action, and ψ and ψ ≡ ψ † γ 0 are ordinary I C 4 -bispinors, the dot meaning derivation with respect to τ . The four Euler-Lagrange equations, with −λ =h = 1, yield the following motion equations:besides the hermitian adjoint of Eq.(2a), holding for ψ. From Eq. (2) one can also see thatis a constant of the motion (and precisely is the energy in the CMF). [8] Since H is the BZ Hamiltonian in the CMF, we can suitably set H = m, where m is the particle rest-mass. The general solution of the equations of motion (3) can be shown to be:with p µ = constant; p 2 = m 2 ; consequently, by inserting Eqs.(5a) and (5b) in the r.h.s. of Eq.(3b), we finally get: Notice that, instead of adopting the variables ψ and ψ, we can work in terms of the "spin variables," i.e., in terms of the set of dynamical variables4 whereis the particle spin tensor; then, we would get the following motion equations:ṗThe last equation expresses the conservation of the total angular momentum J µν , the sum of the orbital angular momentum L µν and of

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The classical problem of the charge and pole motion. A satisfactory formalism by Clifford algebras

Cited by 16 publications

References 11 publications

Hyperbolic Quaternion Formulation of Electromagnetism

Hyperbolic Quaternion Formulation of Electromagnetism

Electromagnetism with magnetic charge and two photons

Hydrodynamical Reformulation and Quantum Limit of the Barut-Zanghi Theory

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