Off-shell electromagnetism in manifestly covariant relativistic quantum mechanics

Saad, David; Horwitz, L. P.; Arshansky, Rafael I

doi:10.1007/bf00731876

Cited by 73 publications

(104 citation statements)

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“…An offshell classical and quantum electrodynamics has been constructed [3] from a fundamental theory of relativistic dynamics of 4D particles, termed events, in a framework first derived by Stueckelberg [1,2]. Stueckelberg defined a Lorentz invariant Hamiltonian-like generator of evolution, over 8D phase space, parameterized by a Lorentz invariant τ , in both classical and quantum relativistic mechanics.…”

Section: Fundamentalsmentioning

confidence: 99%

“…Pre-Maxwell off-shell electrodynamics is constructed in a similar fashion to the construction of Maxwell electrodynamics from the Schrödinger equation [3]. Under the local gauge transformation…”

Section: Off-shell Electrodynamicsmentioning

confidence: 99%

“…In this paper, we concentrate on the construction which from the Stueckelberg framework (cf. [2,3]). …”

Section: Introductionmentioning

confidence: 99%

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Green functions for wave propagation on a five-dimensional manifold and the associated gauge fields generated by a uniformly moving point source

Aharonovich

Horwitz

2006

Journal of Mathematical Physics

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Gauge fields associated with the manifestly covariant dynamics of particles in (3, 1) spacetime are five-dimensional. We provide solutions of the classical 5D gauge field equations in both (4, 1) and (3, 2) flat spacetime metrics for the simple example of a uniformly moving point source. Green functions for the 5D field equations are obtained, which are consistent with the solutions for uniform motion obtained directly from the field equations with free asymptotic conditions.

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Section: Fundamentalsmentioning

confidence: 99%

Section: Off-shell Electrodynamicsmentioning

confidence: 99%

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Green functions for wave propagation on a five-dimensional manifold and the associated gauge fields generated by a uniformly moving point source

Aharonovich

Horwitz

2006

Journal of Mathematical Physics

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“…Analysis of the resulting wave equation [24] for the sourceless case shows that the symmetry group of the equations can be either O(3,2) or O(4,1), depending on the signature of the τ index. Since U α (see ( Since the 4-vector part of the current in (4.14) is not conserved by itself, it may not be the source for the Maxwell field.…”

Section: Implications For Gauge Theory In Covariant Quantum Mechanicsmentioning

confidence: 99%

On Feynman’s approach to the foundations of gauge theory

Land

Shnerb

Horwitz

1995

Journal of Mathematical Physics

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In 1948, Feynman showed Dyson how the Lorentz force law and homogeneous Maxwell equations could be derived from commutation relations among Euclidean coordinates and velocities, without reference to an action or variational principle. When Dyson published the work in 1990, several authors noted that the derived equations have only Galilean symmetry and so are not actually the Maxwell theory. In particular, Hojman and Shepley proved that the existence of commutation relations is a strong assumption, sufficient to determine the corresponding action, which for Feynman's derivation is of Newtonian form. In a recent paper, Tanimura generalized Feynman's derivation to a Lorentz covariant form with scalar evolution parameter, and obtained an expression for the Lorentz force which appears to be consistent with relativistic kinematics and relates the force to the Maxwell field in the usual manner. However, Tanimura's derivation does not lead to the usual Maxwell theory either, because the force equation depends on a fifth (scalar) electromagnetic potential, and the invariant evolution parameter cannot be consistently identified with the proper time of the particle motion. Moreover, the derivation cannot be made reparameterization invariant; the scalar potential causes violations of the mass-shell constraint which this invariance should guarantee.In this paper, we examine Tanimura's derivation in the framework of the proper time method in relativistic mechanics, and use the technique of Hojman and Shepley to study the unconstrained commutation relations. We show that Tanimura's result then corresponds to the five-dimensional electromagnetic theory previously derived from a 1 Stueckelberg-type quantum theory in which one gauges the invariant parameter in the proper time method. This theory provides the final step in Feynman's program of deriving the Maxwell theory from commutation relations; the Maxwell theory emerges as the "correlation limit" of a more general gauge theory, in which it is properly contained.

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“…where j α is given in (19) and (20). Although λ and e 0 must be dimensional constants, the dimensionless ratio e 0 /λ is the Maxwell charge e. In four-vector component form, (24) becomes…”

Section: Gauge Theorymentioning

confidence: 99%

Discrete Symmetries of Off-Shell Electromagnetism

Land

2005

Found Phys

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This paper discusses the discrete symmetries of off-shell electromagnetism, the Stueckelberg-Schrodinger relativistic quantum theory and its associated 5D local gauge theory. Seeking a dynamical description of particle/antiparticle interactions, Stueckelberg developed a covariant mechanics with a monotonically increasing Poincaré-invariant parameter. In Stueckelberg's framework, worldlines are traced out through the parameterized evolution of spacetime events, which may advance or retreat with respect to the laboratory clock, depending on the sign of the energy, so that negative energy trajectories appear as antiparticles when the observer describes the evolution using the laboratory clock. The associated gauge theory describes local interactions between events (correlated by the invariant parameter) mediated by five off-shell gauge fields. These gauge fields are shown to transform tensorially under under space and time reflections -unlike the standard Maxwell fields -and the interacting quantum theory therefore remains manifestly Lorentz covariant. Charge conjugation symmetry in the quantum theory is achieved by simultaneous reflection of the sense of evolution and the fifth scalar field. Applying this procedure to the classical gauge theory leads to a purely classical manifestation of charge conjugation, placing the CP T symmetries on the same footing in the classical and quantum domains. In the resulting picture, interactions do not distinguish between particle and antiparticle trajectories -charge conjugation merely describes the interpretation of observed negative energy trajectories according to the laboratory clock.

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Off-shell electromagnetism in manifestly covariant relativistic quantum mechanics

Cited by 73 publications

References 9 publications

Green functions for wave propagation on a five-dimensional manifold and the associated gauge fields generated by a uniformly moving point source

Green functions for wave propagation on a five-dimensional manifold and the associated gauge fields generated by a uniformly moving point source

On Feynman’s approach to the foundations of gauge theory

Discrete Symmetries of Off-Shell Electromagnetism

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