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The Standard Model (SM) ascribes the observed mass of elementary particles to an effective interaction between basis states defined without mass terms and a scalar potential associated with the Higgs boson. In the relativistic field theory that underlies the SM, mass itself, understood as the Lorentz-invariant squared 4-momentum of a particle or field, is fixed a priori, imposing a constraint on possible momentum states. Stueckelberg introduced an alternative approach, positing antiparticles as particles evolving backward in time, thus relaxing the mass shell constraint for individual particles. Further work by Piron and Horwitz established a covariant Hamiltonian mechanics on an unconstrained 8D phase space, leading to a gauge field theory that mediates the exchange of mass between particles, while the total mass of particles and fields remains conserved. In a recently developed extension of general relativity, consistent with this approach, the spacetime metric evolves in a manner that permits the exchange of mass across spacetime through the gravitational field. Mechanisms that restrict mass exchange between particles have also been identified. Nevertheless, mass exchange remains possible under certain circumstances and may have phenomenological implications in particle physics and cosmology., Comment: 15 pages, 2 figures, prepared for Proceeding of XXIV Bled Workshop "What Comes Beyond the Standard Model?" Bled, July 5-11 2021

The kinematics of pre-Maxwell electrodynamics is examined and interpretations of these fields is found through an examination of the associated Lorentz force and the structure of the energy-momentum tensor., Comment: An updated version of an old paper, posted to arXiv for accessability

This multi-method study examines the differences in male and female computer use in the home of children ages 9-14. Long interviews, observations, and surveys with children show males spend more time on the computer, but not on-line, than females. Males and females engage in different computer activities. They play computer games about the same amount of time, but females spend more time on the computer to do word processing and desk-top publishing activities. Males play more games on-line, while females spend more time on-line to communicate. Contains 13 references and 12 tables of data. (Author/RS)

This paper examines the Stark effect, as a first order perturbation of manifestly covariant hydrogen-like bound states. These bound states are solutions to a relativistic Schr\"odinger equation with invariant evolution parameter, and represent mass eigenstates whose eigenvalues correspond to the well-known energy spectrum of the non-relativistic theory. In analogy to the nonrelativistic case, the off-diagonal perturbation leads to a lifting of the degeneracy in the mass spectrum. In the covariant case, not only do the spectral lines split, but they acquire an imaginary part which is lnear in the applied electric field, thus revealing induced bound state decay in first order perturbation theory. This imaginary part results from the coupling of the external field to the non-compact boost generator. In order to recover the conventional first order Stark splitting, we must include a scalar potential term. This term may be understood as a fifth gauge potential, which compensates for dependence of gauge transformations on the invariant evolution parameter., Comment: Latex, 24 pages

Despite the many successes of the relativistic quantum theory developed by Horwitz, et. al., certain difficulties persist in the associated covariant classical mechanics. In this paper, we explore these difficulties through an examination of the classical Coulomb problem in the framework of off-shell electrodynamics. As the local gauge theory of a covariant quantum mechanics with evolution parameter $\tau$, off-shell electrodynamics constitutes a dynamical theory of spacetime events, interacting through five $\tau$-dependent pre-Maxwell potentials. We present a straightforward solution of the classical equations of motion, which is seen to be unsatisfactory, and reveals the essential difficulties in the formalism at the classical level. We then offer a new model of the particle current -- as a certain distribution of the event currents on the worldline -- which eliminates these difficulties and permits comparison of classical off-shell electrodynamics with the standard Maxwell theory. In this model, the ``fixed'' event induces a Yukawa-type potential, permitting a semi-classical identification of the pre-Maxwell time scale $\lambda$ with the inverse mass of the intervening photon. Numerical solutions to the equations of motion are compared with the standard Maxwell solutions, and are seen to coincide when $\lambda \gtrsim 10^{-6}$ seconds, providing an initial estimate of this parameter. It is also demonstrated that the proposed model provides a natural interpretation for the photon mass cut-off required for the renormalizability of the off-shell quantum electrodynamics., Comment: 21 pages, Latex, 3 Postscript figures

More than twenty years have passed since the threads of the `proper time formalism' in covariant classical and quantum mechanics were brought together to construct a canonical formalism for the relativistic mechanics of many particles. Drawing on the work of Fock, Stueckelberg, Nambu, Schwinger, and Feynman, the formalism was raised from the status of a purely formal mathematical technique to a covariant evolution theory for interacting particles. In the context of this theory, solutions have been found for the relativistic bound state problem, classical and quantum scattering in relativistic potentials, as well as applications in statistical mechanics. It has been shown that a generalization of the Maxwell theory is required in order that the electromagnetic interaction be well-posed in the theory. The resulting theory of electromagnetism involves a fifth gauge field introduced to compensate for the dependence of the gauge transformation on the invariant time parameter; permitting such dependence relaxes the requirement that individual particles be on fixed mass shells and allows exchange of mass during scattering. In this paper, we develop the quantum field theory of off-shell electromagnetism, and use it to calculate certain elementary processes, including Compton scattering and M{\o}ller scattering. These calculations lead to {\em qualitative} deviations from the usual scattering cross-sections, which are, however, small effects, but may be visible at small angles near the forward direction. The familiar IR divergence of the M{\o}ller scattering is, moreover, completely regularized., Comment: Requires FEYNMAN.TEX macro for Feynman diagrams. 72 pages

In the context of a relativistic quantum mechanics with invariant evolution parameter, solutions for the relativistic bound state problem have been found, which yield a spectrum for the total mass coinciding with the nonrelativistic Schr\"odinger energy spectrum. These spectra were obtained by choosing an arbitrary spacelike unit vector $n_\mu$ and restricting the support of the eigenfunctions in spacetime to the subspace of the Minkowski measure space, for which $(x_\perp )^2 = [x-(x \cdot n) n ]^2 \geq 0$. In this paper, we examine the Zeeman effect for these bound states, which requires $n_\mu$ to be a dynamical quantity. We recover the usual Zeeman splitting in a manifestly covariant form., Comment: 21 pages, TAUP-2150-94

In 1948, Feynman showed Dyson how the Lorentz force and Maxwell equations could be derived from commutation relations coordinates and velocities. Several authors noted that the derived equations are not Lorentz covariant and so are not the standard 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. Tanimura generalized Feynman's derivation to a Lorentz covariant form, however, this derivation does not lead to the standard Maxwell theory either. Tanimura's force equation depends on a fifth ({\it 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 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., Comment: This is a complete re-write of our paper, using new techniques, with a new section on non-Abelian gauge fields. (36 pages, latex, no figures)