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.

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.

To Restore the Broken Symmetry in the Nonconfining Schwinger Model

1997 ◽  
Vol 12 (31) ◽  
pp. 5625-5637 ◽  
Author(s):  
Anisur Rahaman
Keyword(s):  
Phase Space ◽  
Gauge Symmetry ◽  
Effective Action ◽  
Invariant Theory ◽  
Broken Symmetry ◽  
Quantum Mechanical ◽  
Gauge Invariant ◽  
Schwinger Model ◽  
Proper Extension

A new generalization of the vector Schwinger model is considered where gauge symmetry is broken at the quantum mechanical level. By proper extension of the phase space this broken symmetry has been restored in two different ways. One of these two leads to a BRST-invariant effective action. An equivalent gauge-invariant theory is reformulated even in the usual phase space also.

scholarly journals A scalable realization of local U(1) gauge invariance in cold atomic mixtures

Science ◽  
2020 ◽  
Vol 367 (6482) ◽  
pp. 1128-1130 ◽  
Author(s):  
Alexander Mil ◽  
Torsten V. Zache ◽  
Apoorva Hegde ◽  
Andy Xia ◽  
Rohit P. Bhatt ◽  
...  
Keyword(s):  
Large Scale ◽  
Gauge Theories ◽  
Spatial Dimension ◽  
Gauge Fields ◽  
Quantum Computers ◽  
Computational Techniques ◽  
Quantum Devices ◽  
Gauge Invariant ◽  
Quantum Simulator ◽  
Elementary Building

In the fundamental laws of physics, gauge fields mediate the interaction between charged particles. An example is the quantum theory of electrons interacting with the electromagnetic field, based on U(1) gauge symmetry. Solving such gauge theories is in general a hard problem for classical computational techniques. Although quantum computers suggest a way forward, large-scale digital quantum devices for complex simulations are difficult to build. We propose a scalable analog quantum simulator of a U(1) gauge theory in one spatial dimension. Using interspecies spin-changing collisions in an atomic mixture, we achieve gauge-invariant interactions between matter and gauge fields with spin- and species-independent trapping potentials. We experimentally realize the elementary building block as a key step toward a platform for quantum simulations of continuous gauge theories.

scholarly journals "SCHWINGER MODEL" ON THE FUZZY SPHERE

2010 ◽  
Vol 25 (37) ◽  
pp. 3151-3167 ◽  
Author(s):  
E. HARIKUMAR
Keyword(s):  
Partition Function ◽  
Field Strength ◽  
Dirac Operator ◽  
Path Integral ◽  
Integral Method ◽  
Gauge Fields ◽  
Fuzzy Sphere ◽  
Schwinger Model ◽  
Spinor Fields ◽  
Path Integral Method

In this paper, we construct a model of spinor fields interacting with specific gauge fields on the fuzzy sphere and analyze the chiral symmetry of this "Schwinger model". In constructing the theory of gauge fields interacting with spinors on the fuzzy sphere, we take the approach that the Dirac operator Dq on the q-deformed fuzzy sphere [Formula: see text] is the gauged Dirac operator on the fuzzy sphere. This introduces interaction between spinors and specific one-parameter family of gauge fields. We also show how to express the field strength for this gauge field in terms of the Dirac operators Dq and D alone. Using the path integral method, we have calculated the 2n-point functions of this model and show that, in general, they do not vanish, reflecting the chiral non-invariance of the partition function.

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.

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.

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 THE BERRY PHASE AND MONOPOLES IN NON-ABELIAN GAUGE THEORIES

2002 ◽  
Vol 17 (02) ◽  
pp. 157-174 ◽  
Author(s):  
F. V. GUBAREV ◽  
V. I. ZAKHAROV
Keyword(s):  
Gauge Theory ◽  
Wilson Loop ◽  
Continuum Limit ◽  
Gauge Theories ◽  
Berry Phase ◽  
Quantum Mechanical ◽  
Abelian Gauge ◽  
Dynamical Phase ◽  
Physical Consequences ◽  
The Continuum

We consider the quantum mechanical notion of the geometrical (Berry) phase in SU(2) gauge theory, both in the continuum and on the lattice. It is shown that in the coherent state basis eigenvalues of the Wilson loop operator naturally decompose into the geometrical and dynamical phase factors. Moreover, for each Wilson loop there is a unique choice of U(1) gauge rotations which do not change the value of the Berry phase. Determining this U(1) locally in terms of infinitesimal Wilson loops we define monopole-like defects and study their properties in numerical simulations on the lattice. The construction is gauge dependent, as is common for all known definitions of monopoles. We argue that for physical applications the use of the Lorentz gauge is most appropriate. And, indeed, the constructed monopoles have the correct continuum limit in this gauge. Physical consequences are briefly discussed.

AXIAL-SCHWINGER MODEL

1996 ◽  
Vol 11 (16) ◽  
pp. 2931-2939 ◽  
Author(s):  
R. AMORIM ◽  
J. BARCELOS-NETO ◽  
A. DE SOUZA DUTRA
Keyword(s):  
Path Integral ◽  
Effective Interaction ◽  
Axial Current ◽  
Gauge Fields ◽  
Schwinger Model ◽  
Local Gauge ◽  
Gauge Symmetries ◽  
Integral Technique ◽  
Topological Current

We consider an extension of the axial model where local gauge symmetries are taken into account. The result is a mixing of the axial and Schwinger models. The anomaly of the axial current is calculated by means of the Fujikawa path integral technique and the model is also solved. Besides the well-known features of the particular models (axial and Schwinger) an effective interaction of scalar and gauge fields via a topological current is obtained. This term is responsible for the appearance of massive poles in the propagators that are different from those of both models.

scholarly journals Gauge fields in real and momentum spaces in magnets: monopoles and skyrmions

2012 ◽  
Vol 370 (1981) ◽  
pp. 5806-5819 ◽  
Author(s):  
N. Nagaosa ◽  
X. Z. Yu ◽  
Y. Tokura
Keyword(s):  
Hall Effect ◽  
Gauge Field ◽  
Berry Phase ◽  
Solid Angle ◽  
Spontaneous Magnetization ◽  
Anomalous Hall Effect ◽  
Magnetic Monopoles ◽  
Real Space ◽  
Gauge Fields ◽  
Quantum Mechanical

Electronic states in magnets are characterized by the quantum mechanical Berry phase defined in both the real and momentum spaces. This Berry phase constitutes the gauge fields, i.e. the emergent electromagnetic fields in solids, and affects the motion of the electrons. In momentum space, the band crossings act as the magnetic monopoles, i.e. the sources or sinks of the gauge flux. In real space, the spin textures with non-coplanar spin configurations produce the gauge field by the solid angle leading to the spin chirality. Skyrmion is the representative structure supporting this gauge field. A typical phenomenon reflecting this gauge field is the anomalous Hall effect, i.e. the Hall effect produced by the spontaneous magnetization combined with the relativistic spin–orbit interaction. We discuss a few examples recently studied related to these issues with some new results on skyrmion formation.

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