C. R. Hagen

Effects of nongauge potentials on the spin-1/2 Aharonov-Bohm problem

Some recent work has attempted to show that the singular solutions which are known to occur in the Dirac description of spin-1/2 Aharonov-Bohm scattering can be eliminated by the inclusion of strongly repulsive potentials inside the flux tube. It is shown here that these calculations are generally unreliable since they necessarily require potentials which lead to the occurrence of Kleins paradox. To avoid that difficulty the problem is solved within the framework of the Galilean spin-1/2 wave equation which is free of that particular complication. It is then found that the singular solutions can be eliminated provided that the nongauge potential is made energy dependent. The effect of the inclusion of a Coulomb potential is also considered with the result being that the range of flux parameter for which singular solutions are allowed is only one-half as great as in the pure Aharonov-Bohm limit. Expressions are also obtained for the binding energies which can occur in the combined Aharonov-Bohm-Coulomb system.

Casimir energy of a spherical shell

The Casimir energy for a conducting spherical shell of radius

Casimir energy for spherical boundaries

a

Perturbation theory and the Aharonov-Bohm effect.

is computed using a direct mode summation approach. An essential ingredient is the implementation of a recently proposed method based on Cauchys theorem for an evaluation of the eigenfrequencies of the system. It is shown, however, that this earlier calculation uses an improper set of modes to describe the waves exterior to the sphere. Upon making the necessary corrections and taking care to ensure that no mathematically ill-defined expressions occur, the technique is shown to leave numerical results unaltered while avoiding a longstanding criticism raised against earlier calculations of the Casimir energy.

Perturbative expansion in the Galilean-invariant spin-1/2 Chern-Simons field theory

Calculations of the Casimir energy for spherical geometries which are based on integrations of the stress tensor are critically examined. It is shown that despite their apparent agreement with numerical results obtained from mode summation methods, they are subject to criticism on several points. Specifically, these include (1) an improper application of the stress tensor to spherical boundaries, (2) the neglect of pole terms in contour integrations, and (3) the imposition of inappropriate boundary conditions upon the relevant propagators. A calculation which is based on the stress tensor and which avoids such problems is shown to be possible. It is, however, equivalent to the mode summation method and does not therefore constitute an independent calculation of the Casimir energy. (c) 2000 The American Physical Society.

Soluble field theory with a massless gauge invariant limit

The perturbation theory expansion of the Aharonov-Bohm scattering amplitude has previously been studied in the context of quantum mechanics for spin-0 and spin-1/2 particles as well as in Galilean covariant field theory. This problem is reconsidered in the framework of the model in which the flux line is considered to have a finite radius which is shrunk to zero at the end of the calculation. General agreement with earlier results is obtained but with the advantage of a treatment which unifies all the various subcases.

Lagrangian formulation for arbitrary spin. I. The boson case

A Galilean Chern-Simons field theory is formulated for the case of two interacting spin-1/2 fields of distinct masses M and M{sup {prime}}. A method for the construction of states containing N particles of mass M and N{sup {prime}} particles of mass M{sup {prime}} is given which is subsequently used to display equivalence to the spin-1/2 Aharonov-Bohm effect in the N=N{sup {prime}}=1 sector of the model. The latter is then studied in perturbation theory to determine whether there are divergences in the fourth order (one-loop) diagram. It is found that the contribution of that order is finite (and vanishing) for the case of parallel spin projections while the antiparallel case displays divergences which are known to characterize the spin-0 case in field theory as well as in quantum mechanics. {copyright} {ital 1997} {ital The American Physical Society}

Rotational anomalies without anyons

It is shown that there exists a soluble four parameter model in 1+1 dimensions all of whose propagators can be determined in terms of the corresponding known propagators of the vector coupling theory. Unlike the latter case, however, the limit of a zero bare mass is nonsingular and yields a nontrivial theory with a rigorously unbroken gauge invariance. (c) 2000 The American Physical Society.