Chiral gauge theories on a lattice and application to the chiral Schwinger model

1988 ◽  
Vol 38 (2) ◽  
pp. 618-626 ◽  
Author(s):  
Sinya Aoki
Keyword(s):  
Gauge Theories ◽  
Schwinger Model

scholarly journals SUPERSPACE FORMULATION FOR THE BRST QUANTIZATION OF THE CHIRAL SCHWINGER MODEL

1998 ◽  
Vol 13 (03) ◽  
pp. 493-500 ◽  
Author(s):  
EVERTON M. C. ABREU ◽  
NELSON R. F. BRAGA
Keyword(s):  
Gauge Theories ◽  
Brst Quantization ◽  
Loop Order ◽  
Schwinger Model ◽  
Closed Algebra ◽  
Quantum Action

It has recently been shown that the field–antifield quantization of anomalous irreducible gauge theories with closed algebra can be represented in a BRST superspace where the quantum action at one loop order, including the Wess–Zumino term, and the anomalies show up as components of the same superfield. We show here how the Chiral Schwinger Model can be represented in this formulation.

scholarly journals THE EFFECT OF DIFFERENT REGULATORS IN THE NONLOCAL FIELD–ANTIFIELD QUANTIZATION

2000 ◽  
Vol 15 (08) ◽  
pp. 1207-1224 ◽  
Author(s):  
EVERTON M. C. ABREU
Keyword(s):  
Gauge Theories ◽  
Second Order ◽  
Schwinger Model ◽  
Nonlocal Field ◽  
Nonlocal Regularization ◽  
Made In

Recently it was shown how to regularize the Batalin–Vilkovisky (BV) field–antifield formalism of quantization of gauge theories with the nonlocal regularization (NLR) method. The objective of this work is to make an analysis of the behavior of this NLR formalism, connected to the BV framework, using two different regulators: a simple second order differential regulator and a Fujikawa-like regulator. This analysis has been made in the light of the well-known fact that different regulators can generate different expressions for anomalies that are related by a local counterterm, or that are equivalent after a reparametrization. This has been done by computing precisely the anomaly of the chiral Schwinger model.

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.

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.

WEYL FERMION FUNCTIONAL INTEGRAL AND TWO-DIMENSIONAL GAUGE THEORIES

1990 ◽  
Vol 05 (14) ◽  
pp. 2839-2851
Author(s):  
J.L. ALONSO ◽  
J.L. CORTÉS ◽  
E. RIVAS
Keyword(s):  
Gauge Theory ◽  
Gauge Theories ◽  
Functional Integral ◽  
Integral Approach ◽  
Two Dimensional ◽  
Regularization Scheme ◽  
Schwinger Model ◽  
Left Handed ◽  
Definition Of ◽  
Weyl Fermion

In the path integral approach we introduce a general regularization scheme for a Weyl fermionic measure. This allows us to study the functional integral formulation of a two-dimensional U(1) gauge theory with an arbitrary content of left-handed and right-handed fermions. A particular result is that, in contrast with a regularization of the fermionic measure based on a unique Dirac operator, by taking the Dirac fermionic measure as a product of two independent Weyl fermionic measures a consistent and unitary result can be obtained for the Chiral Schwinger Model (CSM) as a byproduct of the arbitrariness in the definition of the fermionic measure.

Z-Symmetry and Polyakov Loops in Hot Abelian Gauge Theories

1997 ◽  
Vol 12 (06) ◽  
pp. 1205-1214
Author(s):  
G. Grignani ◽  
P. Sodano ◽  
G. Semenoff ◽  
O. Tirkkonen
Keyword(s):  
Gauge Theories ◽  
Polyakov Loop ◽  
The Other ◽  
Fermion Mass ◽  
Abelian Gauge ◽  
Schwinger Model ◽  
Dimensional Parameters ◽  
Bkt Transition ◽  
Lower Dimensional ◽  
Topological Mass

We discuss the Z symmetry of finite temperature QED, which is related to the confinement properties of the theory. We show the correlators of Polyakov loop operators with incommensurate charges can be used as order parameters for this symmetry. The screening or confining properties of lower dimensional abelian gauge theories are analyzed. In the Schwinger model, the Z-symmetry is broken and the system is in a screening phase; with a non-vanishing fermion mass the symmetry is recovered and the system confines. In parity invariant 2+1-dimensional QED, there is a phase transition between phases with unbroken and broken realizations of this symmetry. This confinement–deconfinement transition is of the Berezinskii–Kosterlitz–Thouless (BKT) type. When there is a topological mass the model exhibits a screening phase. However, if the topological mass is much smaller than the other dimensional parameters there is a vestige of the BKT transition separating regions with screening and confining behavior.

Comment on "Chiral gauge theories on a lattice and application to the chiral Schwinger model"

1989 ◽  
Vol 40 (8) ◽  
pp. 2727-2728 ◽  
Author(s):  
Maarten F. L. Golterman ◽  
Donald N. Petcher
Keyword(s):  
Gauge Theories ◽  
Schwinger Model

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.

THE DYNAMIC QUANTIZATION IN APPLICATION TO 2-DIMENSIONAL GAUGE CHIRAL MODELS

1990 ◽  
Vol 05 (11) ◽  
pp. 2117-2143 ◽  
Author(s):  
S. N. VERGELES
Keyword(s):  
Gauge Theories ◽  
Ultraviolet Region ◽  
Quantization Method ◽  
Schwinger Model ◽  
Deep Ultraviolet ◽  
Infinite Set ◽  
Dynamic Variables

The dynamic quantization method suggested in Ref. 1 is developed here, on the basis of which the quantization of non-Abelian chiral Schwinger model is carried out. Under the dynamic quantization the regularization is realized by imposing the infinite set of the second class constraints for the dynamic variables in a deep ultraviolet region and by passing to the Dirac commutational relations. In this way success is achieved in realization of the traditional interpretation of the gauge theories which are known as anomal. The non-Abelian chiral Schwinger model proves to be gauge- and Lorentz-invariant.

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