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C. R. Hagen

Publications and source records attributed to C. R. Hagen.

36 records · Page 2Linked to original sources
arXiv1998

Non-thermalizability of a Quantum Field Theory

The problem of understanding the role of large gauge transformations in thermal field theories has recently inspired a number of studies of a one dimensional field theory. Such work has led to the conclusion that gauge invariance is restored only when the entire perturbation expansion can be summed. A careful reexamination of that model is shown, h0owever, to lead to vastly different conclusions when the constraint implied by the field equations is explicitly taken into account. In particular it is found that none of the relevant propagators has any temperature dependence and that the effective action is essentially trivial. A generalization of the model to include bosons as well as fermions is also solved with qualitatively identical results being obtained.

hep-th↗
arXiv1997

Perturbative Expansion in the Galilean Invariant Spin One-Half Chern-Simons Field Theory

A Galilean Chern-Simons field theory is formulated for the case of two interacting spin-1/2 fields of distinct masses M and M'. A method for the construction of states containing N particles of mass M and N' particles of mass M' is given which is subsequently used to display equivalence to the spin-1/2 Aharonov-Bohm effect in the N = N' =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 zero case in field theory as well as in quantum mechanics.

hep-th↗
arXiv1996

Comment on ``Quantum Phase of Induced Dipoles Moving in a Magnetic Field''

It has recently been suggested that an Aharonov-Bohm phase should be capable of detection using beams of neutral polarizable particles. A more careful analysis of the proposed experiment suffices to show, however, that it cannot be performed regardless of the strength of the external electric and magnetic fields.

quant-ph↗
arXiv1995

Perturbation Theory and the Aharonov-Bohm Effect

The perturbation theory expansion of the Aharonov-Bohm scattering amplitude has previously been studied in the context of quantum mechanics for spin zero and spin-1/2 particles as well 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.

hep-th↗
arXiv1994

Relativistic Aharonov-Bohm-Coulomb Problem

The Aharonov-Bohm effect is analyzed for a spin-1/2 particle in the case that a $1/r$ potential is present. Scalar and vector couplings are each considered. It is found that the approach in which the flux tube is given a finite radius that is taken to zero only after a matching of boundary conditions does not give physically meaningful results. Specifically, the operations of taking the limit of zero flux tube radius and the Galilean limit do not commute. Thus there appears to be no satisfactory solution of the relativistic Aharonov-Bohm-Coulomb problem using the finite radius flux tube method.

hep-th↗
arXiv1994

Dimensionality as a Perturbation Parameter in the Generalized Hydrogen Atom

A recent suggestion has been made that the hydrogen bound state spectrum should not depend on the number of spatial dimensions. It is pointed out here that the uncertainty principle implies that such differences must exist and that a perturbation expansion in the dimensionality parameter yields a precise quantitative confirmation of the effect.

hep-th↗
arXiv1994

Unification of the Soluble Two-dimensional vector coupling models

The general theory of a massless fermion coupled to a massive vector meson in two dimensions is formulated and solved to obtain the complete set of Green's functions. Both vector and axial vector couplings are included. In addition to the boson mass and the two coupling constants, a coefficient which denotes a particular current definition is required for a unique specification of the model. The resulting four parameter theory and its solution are shown to reduce in appropriate limits to all the known soluble models, including in particular the Schwinger model and its axial vector variant.

hep-th↗
arXiv1994

Symmetry Under $α\rightarrow α+ 1$ is Forbidden by Helicity Conservation

The question as to whether helicity conservation in spin one-half Aharonov Bohm scattering is sufficient in itself to determine uniquely the form of the spinor wave function near the origin is examined. Although it is found that a one parameter family of solutions is compatible with this conservation law, there must nonetheless be singular solutions which break the symmetry $α\rightarrow α+1$ required for an anyon interpretation. Thus the free parameter which occurs does not allow one to eliminate the singular solutions even though it does in principle mean that they can be transferred at will between the spin up and spin down configurations.

hep-th↗
arXiv1993

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 Klein's 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 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.

hep-th↗
arXiv1993

Neutron Acceleration in Uniform Electromagnetic Fields

The question as to whether neutron acceleration can occur in uniform electromagnetic fields is examined. Although such an effect has been predicted using the canonical equations of motion some doubt has been raised recently as to whether it is in principle observable for a spin 1/2 particle. To resolve this issue a gedanken experiment is proposed and analyzed using a wave packet construction for the neutron beam. By allowing arbitrary orientation for the neutron spin as well as for the electric and magnetic fields a non vanishing acceleration of the center of the neutron wave packet is found which confirms the predictions of the canonical formalism.

hep-th↗