Light-Front Quantization of the Vector Schwinger Model with a Photon Mass Term in Faddeevian Regularization

Light front field theory: An advanced PrimerWe present an elementary introduction to quantum field theory formulated in terms of Dirac's light front variables. In addition to general principles and methods, a few more specific topics and approaches based on the author's work will be discussed. Most of the discussion deals with massive two-dimensional models formulated in a finite spatial volume starting with a detailed comparison between quantization of massive free fields in the usual field theory and the light front (LF) quantization. We discuss basic properties such as relativistic invariance and causality. After the LF treatment of the soluble Federbush model, a LF approach to spontaneous symmetry breaking is explained and a simple gauge theory - the massive Schwinger model in various gauges is studied. A LF version of bosonization and the massive Thirring model are also discussed. A special chapter is devoted to the method of discretized light cone quantization and its application to calculations of the properties of quantum solitons. The problem of LF zero modes is illustrated with the example of the two-dimensional Yukawa model. Hamiltonian perturbation theory in the LF formulation is derived and applied to a few simple processes to demonstrate its advantages. As a byproduct, it is shown that the LF theory cannot be obtained as a "light-like" limit of the usual field theory quantized on an initial space-like surface. A simple LF formulation of the Higgs mechanism is then given. Since our intention was to provide a treatment of the light front quantization accessible to postgradual students, an effort was made to discuss most of the topics pedagogically and a number of technical details and derivations are contained in the appendices.

Download Full-text

LIGHT-FRONT HAMILTONIAN AND PATH INTEGRAL QUANTIZATION OF VECTOR SCHWINGER MODEL WITH A PHOTON MASS TERM

Modern Physics Letters A ◽

10.1142/s021773231250157x ◽

2012 ◽

Vol 27 (27) ◽

pp. 1250157 ◽

Cited By ~ 1

Author(s):

USHA KULSHRESHTHA

Keyword(s):

Path Integral ◽

Light Cone ◽

Mass Term ◽

Light Front ◽

Light Cone Gauge ◽

Schwinger Model ◽

Path Integral Quantization ◽

New Class ◽

Gauge Fixing ◽

Form Theory

Vector Schwinger model with a mass term for the photon, describing 2D electrodynamics with massless fermions, studied by us recently [U. Kulshreshtha, Mod. Phys. Lett. A22, 2993 (2007); U. Kulshreshtha and D. S. Kulshreshtha, Int. J. Mod. Phys. A22, 6183 (2007); U. Kulshreshtha, PoS LC2008, 008 (2008)], represents a new class of models. This theory becomes gauge-invariant when studied on the light-front. This is in contrast to the instant-form theory which is gauge-non-invariant. In this work, we study the light-front Hamiltonian and path integral quantization of this theory under appropriate light-cone gauge-fixing. The discretized light-cone quantization of the theory where we wish to make contact with the experimentally observational aspects of the theory would be presented in a separate paper.

Download Full-text

VECTOR SCHWINGER MODEL WITH A PHOTON MASS TERM: GAUGE-INVARIANT REFORMULATION, OPERATOR SOLUTIONS AND HAMILTONIAN AND PATH INTEGRAL FORMULATIONS

Modern Physics Letters A ◽

10.1142/s0217732307023663 ◽

2007 ◽

Vol 22 (39) ◽

pp. 2993-3001 ◽

Cited By ~ 10

Author(s):

USHA KULSHRESHTHA

Keyword(s):

Path Integral ◽

Quantum Electrodynamics ◽

Mass Term ◽

Photon Mass ◽

Two Dimensional ◽

Gauge Invariant ◽

Schwinger Model ◽

Left Handed ◽

Stueckelberg Formalism ◽

Massless Fermions

We consider the vector Schwinger model (VSM) describing two-dimensional electrodynamics with massless fermions, where the left-handed and right-handed fermions are coupled to the electromagnetic field with equal couplings, with a mass term for the U(1) gauge field and then study its operator solutions and the Hamiltonian and path integral formulations. We emphasize here that although the VSM has been studied in the literature rather widely but only without a photon mass term (which was a consequence of demanding the regularization for the VSM to be gauge-invariant (GI)). The VSM with a photon mass term is seen to be a gauge-noninvariant (GNI) theory. Using the standard Stueckelberg formalism we then construct a GI theory corresponding to the proposed GNI model. From this reformulated GI theory, we further recover the physical contents of the proposed GNI theory under a very special gauge choice. The theory proposed and studied here presents a new class of models in the two-dimensional quantum electrodynamics with massless fermions but with a photon mass term.

Download Full-text

Hamiltonian, Path Integral and BRST Formulations of the Vector Schwinger Model with a Photon Mass Term with Faddeevian Regularization

International Journal of Theoretical Physics ◽

10.1007/s10773-015-2665-4 ◽

2015 ◽

Vol 55 (1) ◽

pp. 338-360 ◽

Cited By ~ 5

Author(s):

Usha Kulshreshtha ◽

Daya Shankar Kulshreshtha ◽

James P. Vary

Keyword(s):

Path Integral ◽

Hamiltonian Path ◽

Mass Term ◽

Photon Mass ◽

Schwinger Model

Download Full-text

GAUGE-INVARIANT REFORMULATION OF THE VECTOR SCHWINGER MODEL WITH A PHOTON MASS TERM AND ITS HAMILTONIAN, PATH INTEGRAL AND BRST FORMULATIONS

International Journal of Modern Physics A ◽

10.1142/s0217751x07038049 ◽

2007 ◽

Vol 22 (32) ◽

pp. 6183-6201 ◽

Cited By ~ 11

Author(s):

USHA KULSHRESHTHA ◽

D. S. KULSHRESHTHA

Keyword(s):

Path Integral ◽

Quantum Electrodynamics ◽

Hamiltonian Path ◽

Mass Term ◽

Photon Mass ◽

Gauge Invariant ◽

Schwinger Model ◽

Gauge Fixing ◽

Stueckelberg Formalism ◽

Massless Fermions

Using the Stueckelberg formalism, we construct a gauge-invariant version of the vector Schwinger model (VSM) with a photon mass term studied by one of us recently. This model describes two-dimensional massive electrodynamics with massless fermions, where the left-handed and right-handed fermions are coupled to the electromagnetic field with equal couplings. This model describing the 2D massive electrodynamics becomes gauge-noninvariant (GNI). This is in contrast to the case of the massless VSM which is a gauge-invariant (GI) theory (as a consequence of demanding the regularization for the theory to be GI). In this work we first construct a GI theory corresponding to this model describing the 2D massive electrodynamics, using the Stueckelberg formalism and then we recover the physical contents of the original GNI theory studied earlier, under some special gauge choice. We then study the Hamiltonian, path integral and BRST formulations of this GI theory under appropriate gauge-fixing. The theory presents a new class of models in the 2D quantum electrodynamics with massless fermions but with a photon mass term.

Download Full-text