Path integral regularization of QED by means of Stueckelberg fields

With the help of a Stueckelberg field we construct a regularized U(1) gauge invariant action through the introduction of cutoff functions. This action has the property that it converges formally to the unregularized action of QED when the ultraviolet cutoff goes to infinity. Integrating out exactly the Stueckelberg field we obtain a simple effective regularized action, which is fully gauge invariant and gives rise to the same prediction as QED at the tree level and to the one loop order.Comment: LaTeX file, 12 pages, 3 figures. Revised version, to be published in Phys. Lett.

Energy Gaps in a Spacetime Crystal

This paper presents an analysis of the band structure of a spacetime potential lattice created by a standing electromagnetic wave. We show that there are energy band gaps. We estimate the effect, and propose a measurement that could confirm the existence of such phenomena.Comment: 8 pages. 2 figure

Microcanonical Ensemble and Algebra of Conserved Generators for Generalized Quantum Dynamics

It has recently been shown, by application of statistical mechanical methods to determine the canonical ensemble governing the equilibrium distribution of operator initial values, that complex quantum field theory can emerge as a statistical approximation to an underlying generalized quantum dynamics. This result was obtained by an argument based on a Ward identity analogous to the equipartition theorem of classical statistical mechanics. We construct here a microcanonical ensemble which forms the basis of this canonical ensemble. This construction enables us to define the microcanonical entropy and free energy of the field configuration of the equilibrium distribution and to study the stability of the canonical ensemble. We also study the algebraic structure of the conserved generators from which the microcanonical and canonical ensembles are constructed, and the flows they induce on the phase space.Comment: Plain TeX, 18 pages. Corrected report number onl

Fock-Schwinger proper time formalism for p-branes

The theory of the usual, constrained p-branes is embedded into a larger theory in which there is no constraints. In the latter theory the Fock-Schwinger proper time formalism is extended from point-particles to p-branes which can be considered as a points in an infinite dimensional space M. The quantization appears to be straightforward and elegant. The conventional p-brane states are particular stationary solutions to the functional Schr\"odinger equation which describes the evolution of a membrane's state with respect to the invariant evolution parameter $\tau$. It is also shown that states of a lower dimensional p-brane can be considered as particular states of a higher dimensional p-brane.Comment: 6 page

Spectral Function of Fermion Coupled with Massive Vector Boson at Finite Temperature in Gauge Invariant Formalism

We investigate spectral properties of a fermion coupled with a massive gauge boson with a mass m at finite temperature (T) in the perturbation theory. The massive gauge boson is introduced as a U(1) gauge boson in the Stueckelberg formalism with a gauge parameter \alpha. We find that the fermion spectral function has a three-peak structure for T \sim m irrespective of the choice of the gauge parameter, while it tends to have one faint peak at the origin and two peaks corresponding to the normal fermion and anti-plasmino excitations familiar in QED in the hard thermal loop approximation for T \gg m. We show that our formalism successfully describe the fermion spectral function in the whole T region with the correct high-T limit except for the faint peak at the origin, although some care is needed for choice of the gauge parameter for T \gg m. We clarify that for T \sim m, the fermion pole is almost independent of the gauge parameter in the one-loop order, while for T \gg m, the one-loop analysis is valid only for \alpha \ll 1/g where g is the fermion-boson coupling constant, implying that the one-loop analysis can not be valid for large gauge parameters as in the unitary gauge.Comment: 28pages, 11figures. v2: typos fixe

A Chiral Spin Theory in the Framework of an Invariant Evolution Parameter Formalism

We present a formulation for the construction of first order equations which describe particles with spin, in the context of a manifestly covariant relativistic theory governed by an invariant evolution parameter; one obtains a consistent quantized formalism dealing with off-shell particles with spin. Our basic requirement is that the second order equation in the theory is of the Schr\"{o}dinger-Stueckelberg type, which exhibits features of both the Klein-Gordon and Schr\"{o}dinger equations. This requirement restricts the structure of the first order equation, in particular, to a chiral form. One thus obtains, in a natural way, a theory of chiral form for massive particles, which may contain both left and right chiralities, or just one of them. We observe that by iterating the first order system, we are able to obtain second order forms containing the transverse and longitudinal momentum relative to a time-like vector $t_{\mu}t^{\mu}=-1$ used to maintain covariance of the theory. This time-like vector coincides with the one used by Horwitz, Piron, and Reuse to obtain an invariant positive definite space-time scalar product, which permits the construction of an induced representation for states of a particle with spin. We discuss the currents and continuity equations, and show that these equations of motion and their currents are closely related to the spin and convection parts of the Gordon decomposition of the Dirac current. The transverse and longitudinal aspects of the particle are complementary, and can be treated in a unified manner using a tensor product Hilbert space. Introducing the electromagnetic field we find an equation which gives rise to the correct gyromagnetic ratio, and is fully Hermitian under the proposed scalar product. Finally, we show that the original structure of Dirac'sComment: Latex, 61 pages. Minor revisions. To be published in J. Math. Phy

A Chiral Schwinger model, its Constraint Structure and Applications to its Quantization

The Jackiw-Rajaraman version of the chiral Schwinger model is studied as a function of the renormalization parameter. The constraints are obtained and they are used to carry out canonical quantization of the model by means of Dirac brackets. By introducing an additional scalar field, it is shown that the model can be made gauge invariant. The gauge invariant model is quantized by establishing a pair of gauge fixing constraints in order that the method of Dirac can be used.Comment: 18 page

Geometrical approach to the proton spin decomposition

We discuss in detail and from the geometrical point of view the issues of gauge invariance and Lorentz covariance raised by the approach proposed recently by Chen et al. to the proton spin decomposition. We show that the gauge invariance of this approach follows from a mechanism similar to the one used in the famous Stueckelberg trick. Stressing the fact that the Lorentz symmetry does not force the gauge potential to transform as a Lorentz four-vector, we show that the Chen et al. approach is Lorentz covariant provided that one uses the suitable Lorentz transformation law. We also make an attempt to summarize the present situation concerning the proton spin decomposition. We argue that the ongoing debates concern essentially the physical interpretation and are due to the plurality of the adopted pictures. We discuss these different pictures and propose a pragmatic point of view.Comment: 39 pages, 1 figure, updated version to appear in PRD (2013

Gravitational Repulsion within a Black-Hole using the Stueckelberg Quantum Formalism

We wish to study an application of Stueckelberg's relativistic quantum theory in the framework of general relativity. We study the form of the wave equation of a massive body in the presence of a Schwarzschild gravitational field. We treat the mathematical behavior of the wavefunction also around and beyond the horizon (r=2M). Classically, within the horizon, the time component of the metric becomes spacelike and distance from the origin singularity becomes timelike, suggesting an inevitable propagation of all matter within the horizon to a total collapse at r=0. However, the quantum description of the wave function provides a different understanding of the behavior of matter within the horizon. We find that a test particle can almost never be found at the origin and is more probable to be found at the horizon. Matter outside the horizon has a very small wave length and therefore interference effects can be found only on a very small atomic scale. However, within the horizon, matter becomes totally "tachionic" and is potentially "spread" over all space. Small location uncertainties on the atomic scale become large around the horizon, and different mass components of the wave function can therefore interfere on a stellar scale. This interference phenomenon, where the probability of finding matter decreases as a function of the distance from the horizon, appears as an effective gravitational repulsion.Comment: 20 pages, 6 figure

A Massive Non-Abelian Vector Model

The introduction of a Lagrange multiplier field to ensure that the classical equations of motion are satisfied serves to restrict radiative corrections in a model to being only one loop. The consequences of this for a massive non-Abelian vector model are considered.Comment: 8 pages, LaTeX format; further comments added; accepted for publication at the Canadian Journal of Physic