A SIMPLE MANNER FOR THE QUANTIZATION OF ANOMALOUS GAUGE THEORIES

1989 ◽  
Vol 04 (05) ◽  
pp. 501-506
Author(s):  
O. J. KWON ◽  
B. H. CHO ◽  
S. K. KIM ◽  
Y. D. KIM
Keyword(s):  
Path Integral ◽  
Gauge Theories ◽  
Quantum Level ◽  
Integral Formalism ◽  
Simple Manner ◽  
Gauge Invariant ◽  
Massive Vector ◽  
Schwinger Model ◽  
Vector Theory ◽  
Stueckelberg Formalism

The chiral Schwinger model is a massive vector theory at the quantum level. We construct the gauge invariant action using Stueckelberg formalism from this. Then the resulting action is exactly the same as the modified action obtained by path-integral formalism. We propose a simple manner for the quantization of anomalous gauge theories.

GAUGE-INVARIANT QUANTISATION OF CHIRAL GAUGE THEORIES

1990 ◽  
Vol 05 (03) ◽  
pp. 175-182 ◽  
Author(s):  
T. D. KIEU
Keyword(s):  
Path Integral ◽  
Gauge Theories ◽  
Berry Phase ◽  
Integral Functional ◽  
Gauge Fields ◽  
Quantum Mechanical ◽  
Gauge Invariant ◽  
Normal Ordering ◽  
Schwinger Model ◽  
Holomorphic Representation

The path-integral functional of chiral gauge theories with background gauge potentials are derived in the holomorphic representation. Justification is provided, from first quantum mechanical principles, for the appearance of a functional phase factor of the gauge fields in order to maintain the gauge invariance. This term is shown to originate either from the Berry phase of the first-quantized hamiltonians or from the normal ordering of the second-quantized hamiltonian with respect to the Dirac in-vacuum. The quantization of the chiral Schwinger model is taken as an example.

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

2007 ◽  
Vol 22 (39) ◽  
pp. 2993-3001 ◽  
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.

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

2007 ◽  
Vol 22 (32) ◽  
pp. 6183-6201 ◽  
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.

scholarly journals QUANTUM NONDEMOLITION MEASUREMENTS OF A PARTICLE IN ELECTRIC AND GRAVITATIONAL FIELDS

2001 ◽  
Vol 10 (06) ◽  
pp. 859-868 ◽  
Author(s):  
A. CAMACHO ◽  
A. CAMACHO-GALVÁN
Keyword(s):  
Charged Particle ◽  
Path Integral ◽  
Equivalence Principle ◽  
Continuous Monitoring ◽  
Spherical Body ◽  
Quantum Level ◽  
Integral Formalism ◽  
Measuring Device ◽  
Gravitational Fields ◽  
Quantum Nondemolition

In this work we obtain a nondemolition variable for the case in which a charged particle moves in the electric and gravitational fields of a spherical body. Afterwards we consider the continuous monitoring of this nondemolition parameter, and calculate, along the ideas of the so called restricted path integral formalism, the corresponding propagator. Using these results the probabilities associated with the possible measurement outputs are evaluated. The limit of our results, as the resolution of the measuring device goes to zero, is analyzed, and the dependence of the corresponding propagator upon the strength of the electric and gravitational fields is commented. The role that mass plays in the corresponding results, and its possible connection with the equivalence principle at quantum level, are studied.

ON THE WESS-ZUMINO TERM FOR A GENERAL ANOMALOUS GAUGE THEORY WITH SECOND CLASS CONSTRAINTS

1990 ◽  
Vol 05 (06) ◽  
pp. 1123-1133 ◽  
Author(s):  
C. WOTZASEK
Keyword(s):  
Gauge Theory ◽  
Degrees Of Freedom ◽  
Gauge Theories ◽  
Vector Boson ◽  
Boson Field ◽  
Massive Vector ◽  
Schwinger Model ◽  
Working Out

We proposed an algorithm to modify anomalous gauge theories by inserting new degrees of freedom in the system which transforms the constraints from second to first class. We illustrate this technique working out the cases of a massive vector boson field and the chiral Schwinger model.

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.

θ VACUUM IN THE CHIRAL SCHWINGER MODEL

1991 ◽  
Vol 06 (02) ◽  
pp. 243-261 ◽  
Author(s):  
M. CARENA ◽  
C.E.M. WAGNER
Keyword(s):  
Physical Properties ◽  
Vacuum State ◽  
Cluster Property ◽  
Gauge Invariant ◽  
Schwinger Model ◽  
Invariant Formulation ◽  
Dependent Parameter ◽  
Vector Theory ◽  
Θ Vacuum

The physical properties of the chiral Schwinger model are studied, for the particular value of the regularization-dependent parameter a=2. Within a gauge-invariant formulation, we prove that, apart from free physical chiral states, the chiral Schwinger model is equivalent to the vector Schwinger model. In particular, we show that, as in the vector theory, the cluster property is not fulfilled unless the vacuum state is properly defined.

ISOMORPHIC REPRESENTATIONS OF ANOMALOUS CHIRAL GAUGE THEORIES

1989 ◽  
Vol 04 (12) ◽  
pp. 3041-3055 ◽  
Author(s):  
H.O. GIROTTI ◽  
K.D. ROTHE
Keyword(s):  
Gauge Theories ◽  
Hamiltonian Formalism ◽  
Gauge Invariant ◽  
Schwinger Model

Anomalous chiral gauge theories allow for gauge invariant and gauge noninvariant descriptions. We show that these are isomorphic and use this result to comment on misinterpretations of some aspects of the chiral Schwinger model. We also use this model to demonstrate how the isomorphism emerges within the Hamiltonian formalism.

scholarly journals THE SCHWINGER MODEL ON A CIRCLE: RELATION BETWEEN PATH INTEGRAL AND HAMILTONIAN APPROACHES

2006 ◽  
Vol 21 (32) ◽  
pp. 6593-6619 ◽  
Author(s):  
S. AZAKOV
Keyword(s):  
Path Integral ◽  
Correlation Functions ◽  
Hamiltonian Formalism ◽  
Analytical Continuation ◽  
Spectral Flow ◽  
Integral Formalism ◽  
Schwinger Model ◽  
Path Integral Formalism

We solve the massless Schwinger model exactly in Hamiltonian formalism on a circle. We construct physical states explicitly and discuss the role of the spectral flow and nonperturbative vacua. Different thermodynamical correlation functions are calculated and after performing the analytical continuation are compared with the corresponding expressions obtained for the Schwinger model on the torus in Euclidean path integral formalism obtained before.

scholarly journals AN EQUIVALENCE OF TWO MASS GENERATION MECHANISMS FOR GAUGE FIELDS

2008 ◽  
Vol 23 (13) ◽  
pp. 1973-1993
Author(s):  
ALEXEY SEVOSTYANOV
Keyword(s):  
Gauge Theories ◽  
Generation Mechanism ◽  
Gauge Fields ◽  
Quantum Field ◽  
Mass Generation ◽  
Gauge Invariant ◽  
Massive Vector ◽  
Abelian Case ◽  
Generation Mechanisms ◽  
Topological Mass

Two mass generation mechanisms for gauge theories are studied. It is proved that in the Abelian case the topological mass generation mechanism introduced in Refs. 4, 12 and 15 is equivalent to the mass generation mechanism defined in Refs. 5 and 20 with the help of "localization" of a nonlocal gauge invariant action. In the non-Abelian case the former mechanism is known to generate a unitary renormalizable quantum field theory, describing a massive vector field.

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