PATH INTEGRAL QUANTIZATION OF THE CHIRAL SCHWINGER MODEL IN BOSONIZED FORM

2008 ◽  
Vol 23 (27n28) ◽  
pp. 4517-4532 ◽  
Author(s):  
PAUL BRACKEN
Keyword(s):  
Path Integral ◽  
Gauge Invariance ◽  
Path Integrals ◽  
Integral Approach ◽  
Gauge Invariant ◽  
Schwinger Model ◽  
Path Integral Quantization ◽  
Path Integral Approach ◽  
Physical Quantities

The development of the Wess–Zumino action or one-cycle is reviewed from the path integral approach. This is related to the occurrence of anomalies in the theory, and generally signifies a breakdown of gauge invariance. The Jackiw–Rajaraman version of the chiral Schwinger model is studied by means of path integrals. It is shown how the model can be made gauge invariant by using a Wess–Zumino term to write a gauge invariant Lagrangian. The model is considered only in bosonized form without any reference to fermions. The constraints are determined. These components are then used to write a path integral quantization for the bosonized form of the model. Some physical quantities and information, in particular, propagators are derived from the path integral.

scholarly journals GENERALIZED HAMILTONIAN EMBEDDING OF THE PROCA MODEL

1996 ◽  
Vol 11 (24) ◽  
pp. 1919-1927 ◽  
Author(s):  
N. BANERJEE ◽  
R. BANERJEE
Keyword(s):  
Path Integral ◽  
Maxwell Field ◽  
Integral Approach ◽  
Gauge Invariant ◽  
Class Theory ◽  
Path Integral Approach ◽  
Basic Set ◽  
Embedded Model ◽  
Form Field

We convert the second-class Proca model into a first-class theory by using the generalized prescription of Batalin, Fradkin and Tyutin. We then show how a basic set of gauge-invariant fields in the embedded model can be identified with the fundamental fields in the Proca model as well as with the observables in the Stückelberg model or in the model involving the interaction of an Abelian two-form field with the Maxwell field. The connection of these models with the massive Kalb–Ramond model is also elucidated within a path integral approach.

A NOVEL COVARIANT APPROACH TO THE QUANTIZATION OF INTERACTIVE CHIRAL BOSONS

1994 ◽  
Vol 09 (14) ◽  
pp. 1273-1281 ◽  
Author(s):  
JIAN-GE ZHOU ◽  
YAN-GANG MIAO ◽  
YAO-YANG LIU
Keyword(s):  
Path Integral ◽  
Integral Approach ◽  
Gauge Fields ◽  
Covariant Quantization ◽  
Covariant Approach ◽  
Schwinger Model ◽  
Path Integral Approach ◽  
Chiral Bosons

A new covariant quantization of chiral bosons in the chiral Schwinger model with faddeevian regularization is carried out from Batalin-Fradkin (BF) algorithm. In order to turn the second class chiral constraint into first class constraints, infinitely many BF fields are first introduced. When combined with Batalin-Fradkin-Vilkovisky (BFV) formalism, two kinds of BRST-invariant actions have been derived. The first contains the Wess-Zumino action induced from the usual path-integral approach. But the second includes Wotzasek’s Wess-Zumino action coupled to the gauge fields.

Dimensional regularization and the path-integral approach to photon mass in the Schwinger model

1989 ◽  
Vol 67 (5) ◽  
pp. 515-518
Author(s):  
T. F. Treml
Keyword(s):  
Path Integral ◽  
Quantum Electrodynamics ◽  
Dimensional Regularization ◽  
Integral Approach ◽  
Coordinate Space ◽  
Photon Mass ◽  
Two Dimensional ◽  
Schwinger Model ◽  
Path Integral Approach

The derivation of the photon mass in the Schwinger model (two-dimensional quantum electrodynamics) is studied in a path-integral approach that employs a coordinate-space form of dimensional regularization. The role of the antisymmetric epsilon pseudotensor in dimensional regularization is briefly discussed. It is shown that the correct photon mass may easily be recovered by a dimensionally regularized calculation in which the epsilon pseudotensor is taken to be a purely two-dimensional quantity.

scholarly journals DEPARAMETRIZATION AND QUANTIZATION OF THE TAUB UNIVERSE

2002 ◽  
Vol 17 (21) ◽  
pp. 2885-2896 ◽  
Author(s):  
GASTÓN GIRIBET ◽  
CLAUDIO SIMEONE
Keyword(s):  
Path Integral ◽  
Previous Analysis ◽  
Transition Amplitude ◽  
Cosmological Models ◽  
Integral Approach ◽  
Anisotropic Universe ◽  
Formal Expression ◽  
Path Integral Quantization ◽  
Path Integral Approach ◽  
Intrinsic Time

Previous analysis about the deparametrization and path integral quantization of cosmological models are extended to models which do not admit an intrinsic time. The formal expression for the transition amplitude is written down for the Taub anisotropic universe with a clear notion of time. The relation existing between the deparametrization associated to gauge fixation required in the path integral approach and the procedure of reduction of the Wheeler–DeWitt equation is also studied.

THE PATH INTEGRAL APPROACH TO AN N-PARTICLE IN A PT-SYMMETRIC HARMONIC OSCILLATOR

2010 ◽  
Vol 24 (28) ◽  
pp. 5579-5587
Author(s):  
SIKARIN YOO-KONG
Keyword(s):  
Harmonic Oscillator ◽  
Total Energy ◽  
Path Integral ◽  
Path Integrals ◽  
Harmonic Potential ◽  
Integral Approach ◽  
Path Integral Approach ◽  
System Of Particles

We study a path integral approach to a system of particles in a PT-symmetric harmonic potential: V(x)=mω2(x2±2iεx)/2. The eigenvalues and eigenstates of the system have been calculated. We find that the total energy of the system is real. The connection between the non-Hermitian and Hermitian Hamiltonians has been discussed and we also establish this connection in the context of path integrals via a considering model.

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

2012 ◽  
Vol 27 (27) ◽  
pp. 1250157 ◽  
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.

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