TY - JOUR

T1 - Off-shell electromagnetism in manifestly covariant relativistic quantum mechanics

AU - Saad, David

AU - Horwitz, L. P.

AU - Arshansky, R. I.

PY - 1989/10

Y1 - 1989/10

N2 - Gauge invariance of a manifestly covariant relativistic quantum theory with evolution according to an invariant time τ implies the existence of five gauge compensation fields, which we shall call pre-Maxwell fields. A Lagrangian which generates the equations of motion for the matter field (coinciding with the Schrödinger type quantum evolution equation) as well as equations, on a five-dimensional manifold, for the gauge fields, is written. It is shown that τ integration of the equations for the pre-Maxwell fields results in the usual Maxwell equations with conserved current source. The analog of the O (3, 1) symmetry of the usual Maxwell theory is found to be O (3, 2) or O (4, 1), depending on the space-time Fourier spectrum of the field. We argue that the structure that is relevant to the description of radiation in interaction with matter evolving in a timelike sense is that of O (3, 2). The noncovariant form of the field equations is given; there are two fields of electric type and one (divergenceless) magnetic type field. The Noether currents are studied, and some remarks are made on second quantization.

AB - Gauge invariance of a manifestly covariant relativistic quantum theory with evolution according to an invariant time τ implies the existence of five gauge compensation fields, which we shall call pre-Maxwell fields. A Lagrangian which generates the equations of motion for the matter field (coinciding with the Schrödinger type quantum evolution equation) as well as equations, on a five-dimensional manifold, for the gauge fields, is written. It is shown that τ integration of the equations for the pre-Maxwell fields results in the usual Maxwell equations with conserved current source. The analog of the O (3, 1) symmetry of the usual Maxwell theory is found to be O (3, 2) or O (4, 1), depending on the space-time Fourier spectrum of the field. We argue that the structure that is relevant to the description of radiation in interaction with matter evolving in a timelike sense is that of O (3, 2). The noncovariant form of the field equations is given; there are two fields of electric type and one (divergenceless) magnetic type field. The Noether currents are studied, and some remarks are made on second quantization.

UR - http://www.scopus.com/inward/record.url?scp=0003824673&partnerID=8YFLogxK

U2 - 10.1007/BF00731876

DO - 10.1007/BF00731876

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AN - SCOPUS:0003824673

SN - 0015-9018

VL - 19

SP - 1125

EP - 1149

JO - Foundations of Physics

JF - Foundations of Physics

IS - 10

ER -