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. (shrink)

Thought experiments analogous to those discussed by Landau and Peierls are studied in the framework of a manifestly covariant relativistic quantum theory. It is shown that momentum and energy can be arbitrarily well defined, and that the drifts induced by measurement in the positions and times of occurrence of events remain within the (stable) spread of the wave packet in space-time. The structure of the Newton-Wigner position operator is studied in this framework, and it is shown that an analogous time (...) operator can be constructed which satisfies the canonical commutation relation with the energy E but does not commute (due to the presence of a time drift term) with the momentum p. The resulting commutation relation is used as a mathematical basis for the derivation of the Landau-Peierls relation Δt Δp≳ħ/c. (shrink)

Recently, in the framework of a relativistic quantum theory with invariant evolution parameter, solutions have been found for the two-body bound state, whose mass spectrum agrees with the nonrelativistic Schrödinger energy spectrum. In this paper, we study the radiative transitions of these states in the dipole approximation and find that the selection rules are identical with those of the usual nonrelativistic theory, expressed in a manifestly covariant form. In addition to the transverse and longitudinal polarizations of the nonrelativistic theory, we (...) find a “scalar” transition, induced by the relative time coordinate, which is of the same type as the longitudinal transition, expressing the Lorentz covariance of the theory. (shrink)

We show the existence of Lorentz invariant Berry phases generated, in the Stueckelberg–Horwitz–Piron manifestly covariant quantum theory (SHP), by a perturbed four dimensional harmonic oscillator. These phases are associated with a fractional perturbation of the azimuthal symmetry of the oscillator. They are computed numerically by using time independent perturbation theory and the definition of the Berry phase generalized to the framework of SHP relativistic quantum theory.

The dynamical equations of relativistic quantum mechanics prescribe the motion of wave packets for sets of events which trace out the world lines of the interacting particles. Electromagnetic theory suggests thatparticle world line densities be constructed from concatenation of event wave packets. These sequences are realized in terms of conserved probability currents. We show that these conserved currents provide a consistent particle and antiparticle interpretation for the asymptotic states in scattering processes. The relation between current conservation and unitarity is used (...) to establish relations between pair production and annihilation amplitudes and scattering. The discrete symmetriesC, T, P are studied and it is shown that no Dirac sea (for fermions where such a construction is possible, or bosons where it is not) is required for consistency of the theory. These currents, furthermore, represent the discrete symmetries in a way consistent with their interpretation as particle currents. (shrink)

The contemporary view of the fundamental role of time in physics generally ignores its most obvious characteric, namely its flow. Studies in the foundations of relativistic mechanics during the past decade have shown that the dynamical evolution of a system can be treated in a manifestly covariant way, in terms of the solution of a system of canonical Hamilton type equations, by considering the space-time coordinates and momenta ofevents as its fundamental description. The evolution of the events, as functions of (...) a universal invariant world, or historical, time, traces out the world lines that represent the phenomena (e.g., particles) which are observed in the laboratory. The positions in time of each of the events, i.e., the time of their potential detection, are, in this framework, controlled by this universal parameter τ, the time at which they are generated (and may proceed in the positive or negative sense). We find that the notion of thestate of a system requires generalization; at any given τ, it involves information about the system at timest(τ) ≠ τ. The correlation of what may be measured att(τ) with what is generated at τ is necessarily quite rigid, and is related covariantly to the spacelike correlations found in interference experiments. We find, furthermore, that interaction with Maxwell electromagnetism leads back to a static picture of the world, with no real evolution. As a consequence of this result, and the requirement of gauge invariance for the quantum mechanical evolution equation, we conclude that electromagnetism is described by a pre-Maxwell field, whose τ-integral (or asymptotic behavior as τ → ∞) may be identified with the Maxwell field. We therefore consider the world of events in space time, interacting through τ-dependent pre-Maxwell fields, as far as electrodynamics is concerned, as the objective dynamical reality. Our perception of the world, through laboratory detectors and our eyes, are based onintegration over τ over intervals sufficiently large to obtain an aposteriori description of the phenomena which coincides with the Maxwell theory. Fundamental notions, such as the conservation of charge, rest on this construction. The decomposition of the common notion of time into two essentially different aspects, one associated with an unvarying flow, and the second with direct observation subject to dynamical modification, has profound philosophical consequences, of which we are able to explore here only a few. (shrink)