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.

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.

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 EXTENSION OF CHERN–SIMONS FORMS AND NEW GAUGE ANOMALIES

2014 ◽  
Vol 29 (03n04) ◽  
pp. 1450027 ◽  
Author(s):  
IGNATIOS ANTONIADIS ◽  
GEORGE SAVVIDY
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Gauge Field Theories ◽  
Field Theories ◽  
Gauge Fields ◽  
Quantum Field ◽  
Gauge Invariant ◽  
Higher Rank ◽  
Gauge Anomalies ◽  
Chern Simons

We present a general analysis of gauge invariant, exact and metric independent forms which can be constructed using higher-rank field-strength tensors. The integrals of these forms over the corresponding space–time coordinates provides new topological Lagrangians. With these Lagrangians one can define gauge field theories which generalize the Chern–Simons quantum field theory. We also present explicit expressions for the potential gauge anomalies associated with the tensor gauge fields and classify all possible anomalies that can appear in lower dimensions.

scholarly journals On classical and quantum deformations of gauge theories

2021 ◽  
Vol 81 (9) ◽  
Author(s):  
I. L. Buchbinder ◽  
P. M. Lavrov
Keyword(s):  
Gauge Theory ◽  
Gauge Theories ◽  
Gauge Fields ◽  
Exact Relation ◽  
Gauge Invariant ◽  
Gauge Algebra ◽  
Local Functions ◽  
Quantum Deformations ◽  
Non Local ◽  
The Given

AbstractWe elaborate the generalizations of the approach to gauge-invariant deformations of the gauge theories developed in our previous work (Buchbinder and Lavrov in JHEP 06:097, 2021). In the given paper we construct the exact transformations defying the gauge-invariant deformed theory on the base of initial gauge theory with irreducible open gauge algebra. Like in [1], for the theories with open gauge algebras these transformations are the shifts of the initial gauge fields $$A \rightarrow A+h(A)$$ A → A + h ( A ) , with the help of the arbitrary and in general non-local functions h(A). The results are applied to study the quantum aspects of the deformed theories. We derive the exact relation between the quantum effective actions for the above classical theories, where one is obtained from another with the help of the deformation.

scholarly journals EFFECTIVE ACTION OF SPONTANEOUSLY BROKEN GAUGE THEORIES

1998 ◽  
Vol 13 (01) ◽  
pp. 95-124 ◽  
Author(s):  
S.-H. HENRY TYE ◽  
YAN VTOROV-KAREVSKY
Keyword(s):  
Effective Potential ◽  
Effective Action ◽  
Gauge Theories ◽  
Perturbation Expansion ◽  
Gauge Invariant ◽  
Abelian Case ◽  
Covariant Gauge ◽  
The One ◽  
Higgs Fields ◽  
Field Redefinition

The effective action of a Higgs theory should be gauge-invariant. However, the quantum and/or thermal contributions to the effective potential seem to be gauge-dependent, posing a problem for its physical interpretation. In this paper, we identify the source of the problem and argue that in a Higgs theory perturbative contributions should be evaluated with the Higgs fields in the polar basis, not in the Cartesian basis. Formally, this observation can be made from the derivation of the Higgs theorem, which we provide. We show explicitly that, properly defined, the effective action for the Abelian Higgs theory is gauge-invariant to all orders in perturbation expansion when evaluated in the covariant gauge in the polar basis. In particular, the effective potential is gauge-invariant. We also show the equivalence between the calculations in the covariant gauge in the polar basis and the unitary gauge. These points are illustrated explicitly with the one-loop calculations of the effective action. With a field redefinition, we obtain the physical effective potential. The SU(2) non-Abelian case is also discussed.

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.

scholarly journals Renormalized Schwinger–Dyson functional

2021 ◽  
Vol 81 (2) ◽  
Author(s):  
Enore Guadagnini ◽  
Vittoria Urso
Keyword(s):  
Gauge Theories ◽  
Gauge Fields ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Renormalization Procedure ◽  
Expectation Values ◽  
Generating Functional ◽  
Perturbative Renormalization ◽  
The Relationship ◽  
Chern Simons

AbstractWe consider the perturbative renormalization of the Schwinger–Dyson functional, which is the generating functional of the expectation values of the products of the composite operator given by the field derivative of the action. It is argued that this functional plays an important role in the topological Chern–Simons and BF quantum field theories. It is shown that, by means of the renormalized perturbation theory, a canonical renormalization procedure for the Schwinger–Dyson functional is obtained. The combinatoric structure of the Feynman diagrams is illustrated in the case of scalar models. For the Chern–Simons and the BF gauge theories, the relationship between the renormalized Schwinger–Dyson functional and the generating functional of the correlation functions of the gauge fields is produced.

scholarly journals Vector–Tensor Duality

1997 ◽  
Vol 12 (35) ◽  
pp. 2699-2705 ◽  
Author(s):  
Amitabha Lahiri
Keyword(s):  
Sigma Model ◽  
Nonlinear Sigma Model ◽  
Flat Connection ◽  
Mass Generation ◽  
Goldstone Bosons ◽  
Abelian Case ◽  
Vector Bosons ◽  
Topological Mass

A dynamical non-Abelian two-form potential gives masses to vector bosons via a topological coupling.1 Unlike in the Abelian case, the two-form cannot be dualized to Goldstone bosons. Duality is restored by coupling a flat connection to the theory in a particular way, and the new action is then dualized to a nonlinear sigma model. The presence of the flat connection is crucial, which saves the original mechanism of Higgs-free topological mass generation from being dualized to a sigma model.

COMMENT ON MASS GENERATION IN THE CHIRAL SCHWINGER MODEL

1991 ◽  
Vol 06 (18) ◽  
pp. 1657-1663
Author(s):  
THILO BERGER
Keyword(s):  
Gauge Theory ◽  
Gauge Boson ◽  
Invariant Theory ◽  
Low Energy ◽  
Generation Mechanism ◽  
Mass Generation ◽  
Gauge Invariant ◽  
Schwinger Model ◽  
Energy Version

The mass generation mechanism for the gauge boson in the chiral Schwinger model is compared with one in the vector Schwinger model. They do not differ substantially, and we argue that an anomalous chiral gauge theory should be seen generally as a special low-energy version of a gauge invariant theory.

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