LOCAL GAUGE FIELDS BASED ON A U(1) GAUGE THEORY IN LOOP SPACE

1994 ◽  
Vol 09 (11) ◽  
pp. 1889-1908 ◽  
Author(s):  
SHINICHI DEGUCHI ◽  
TADAHITO NAKAJIMA
Keyword(s):  
Gauge Theory ◽  
Vector Field ◽  
Loop Space ◽  
Tensor Field ◽  
Antisymmetric Tensor ◽  
Quantum Theories ◽  
Massive Vector ◽  
Local Field Theory ◽  
Antisymmetric Tensor Field ◽  
Stueckelberg Formalism

We present a U(1) gauge theory defined in loop space, the space of all loops in Minkowski space. On the basis of the U(1) gauge theory, we derive a local field theory of the second-rank antisymmetric tensor field (Kalb-Ramond field) and the Stueckelberg formalism for a massive vector field; the second-rank antisymmetric tensor field and the massive vector field are regarded as parts of a U(1) gauge field on the loop space. We also consider the quantum theories of the second-rank antisymmetric tensor field and the massive vector field on the basis of a BRST formalism for the U(1) gauge theory in loop space. In addition, reparametrization invariance in the U(1) gauge theory is discussed in detail.

HAMILTONIAN BRST QUANTIZATION OF AN ABELIAN MASSIVE VECTOR FIELD WITH AN ANTISYMMETRIC TENSOR FIELD

1995 ◽  
Vol 10 (10) ◽  
pp. 813-822 ◽  
Author(s):  
HIROHUMI SAWAYANAGI
Keyword(s):  
Vector Field ◽  
Tensor Field ◽  
Brst Quantization ◽  
Antisymmetric Tensor ◽  
Massive Vector ◽  
Fixed Action ◽  
Antisymmetric Tensor Field ◽  
Covariant Gauge ◽  
New Variables

The Lagrangian of an Abelian massive vector field gives a system with second class constraints. We apply the Batalin–Fradkin formalism, which converts second class constraints to first class ones through the introduction of new variables. As a new variable, instead of the Stueckelberg field, we introduce an antisymmetric tensor field. A covariant gauge-fixed action is presented. The unitarity and the duality are also discussed.

scholarly journals ON THE TENSOR FORMULATION OF EFFECTIVE VECTOR LAGRANGIANS AND DUALITY TRANSFORMATIONS

1996 ◽  
Vol 11 (13) ◽  
pp. 1069-1080 ◽  
Author(s):  
JOHAN BIJNENS ◽  
ELISABETTA PALLANTE
Keyword(s):  
Vector Field ◽  
Tensor Field ◽  
Axial Vector ◽  
Antisymmetric Tensor ◽  
Vector Mesons ◽  
Massive Vector ◽  
Duality Transformations ◽  
Effective Lagrangian ◽  
Antisymmetric Tensor Field ◽  
Tensor Formulation

Using two different methods inspired by duality transformations we present the equivalence between effective Lagrangians for massive vector mesons using a vector field and an antisymmetric tensor field. This completes the list of explicit field transformations between the various effective Lagrangian methods to describe massive vector and axial vector mesons. Our method automatically generates the point-like terms needed for off-shell equivalence.

scholarly journals A Yang–Mills Theory in Loop Space and Chapline–Manton Coupling

1997 ◽  
Vol 12 (02) ◽  
pp. 111-119 ◽  
Author(s):  
Shinichi Deguchi ◽  
Tadahito Nakajima
Keyword(s):  
Field Theory ◽  
Local Field ◽  
Loop Space ◽  
Tensor Field ◽  
Symmetric Tensor ◽  
Tensor Fields ◽  
Yang Mills ◽  
Local Field Theory ◽  
Antisymmetric Tensor Field ◽  
Chern Simons

We consider a Yang–Mills theory in loop space with the affine gauge group. From this theory, we derive a local field theory with Yang–Mills fields and Abelian antisymmetric and symmetric tensor fields of the second rank. The Chapline–Manton coupling, i.e. coupling of Yang–Mills fields and a second-rank antisymmetric tensor field via the Chern–Simons three-form is obtained systematically.

scholarly journals A SUPERSPACE FORMULATION OF ABELIAN ANTISYMMETRIC TENSOR GAUGE THEORY

2000 ◽  
Vol 15 (15) ◽  
pp. 965-978 ◽  
Author(s):  
SHINICHI DEGUCHI ◽  
BHABANI PRASAD MANDAL
Keyword(s):  
Gauge Theory ◽  
Tensor Field ◽  
Ad Hoc ◽  
Compact Form ◽  
Antisymmetric Tensor ◽  
Lagrange Equations ◽  
Generating Functional ◽  
Transformation Rules ◽  
Antisymmetric Tensor Field ◽  
Rank 2

We apply a superspace formulation to the four-dimensional gauge theory of a massless Abelian antisymmetric tensor field of rank 2. The theory is formulated in a six-dimensional superspace using rank-2 tensor, vector and scalar superfields and their associated supersources. It is shown that BRS transformation rules of fields are realized as Euler–Lagrange equations without assuming the so-called horizontality condition in an ad hoc manner and that a generating functional [Formula: see text] constructed in the superspace reduces to that of the ordinary gauge theory of Abelian rank-2 antisymmetric tensor field. The WT identity for this theory is derived by making use of the superspace formulation and is expressed in a neat and compact form [Formula: see text].

scholarly journals GAUGE INVARIANCES IN THE PROCA MODEL

1998 ◽  
Vol 13 (05) ◽  
pp. 765-778 ◽  
Author(s):  
A. S. VYTHEESWARAN
Keyword(s):  
Gauge Theory ◽  
Phase Space ◽  
Projection Operator ◽  
Tensor Field ◽  
Gauge Theories ◽  
Lorentz Invariance ◽  
Maxwell Field ◽  
Antisymmetric Tensor ◽  
Antisymmetric Tensor Field

We show that the Abelian Proca model, which is gauge noninvariant with second class constraints can be converted into gauge theories with first class constraints. The method used, which we call gauge unfixing, employs a projection operator defined in the original phase space. This operator can be constructed in more than one way and so we get more than one gauge theory. Two such gauge theories are the Stückelberg theory and the theory of Maxwell field interacting with an antisymmetric tensor field. We also show that the application of the projection operator does not affect the Lorentz invariance of this model.

scholarly journals THE FINITENESS OF THE FOUR-DIMENSIONAL ANTISYMMETRIC TENSOR FIELD MODEL IN A CURVED BACKGROUND

1998 ◽  
Vol 13 (26) ◽  
pp. 4513-4537
Author(s):  
U. FEICHTINGER ◽  
O. MORITSCH ◽  
J. RANT ◽  
M. SCHWEDA ◽  
H. ZERROUKI
Keyword(s):  
Perturbation Theory ◽  
Vector Field ◽  
Tensor Field ◽  
Field Model ◽  
Antisymmetric Tensor ◽  
Vector Parameter ◽  
Constant Vector ◽  
Curved Space ◽  
Closed Algebra ◽  
Antisymmetric Tensor Field

A renormalizable rigid supersymmetry for the four-dimensional antisymmetric tensor field model in a curved space–time background is constructed. A closed algebra between the BRS and the supersymmetry operators is only realizable if the vector parameter of the supersymmetry is a covariantly constant vector field. This also guarantees that the corresponding transformations lead to a genuine symmetry of the model. The proof of the ultraviolet finiteness to all orders of perturbation theory is performed in a pure algebraic manner by using the rigid supersymmetry.

scholarly journals On the quantum equivalence of an antisymmetric tensor field with spontaneous Lorentz violation

2020 ◽  
Vol 35 (12) ◽  
pp. 2050087 ◽  
Author(s):  
Sandeep Aashish ◽  
Sukanta Panda
Keyword(s):  
Vector Field ◽  
Minimal Model ◽  
Tensor Field ◽  
Field Model ◽  
Lorentz Violation ◽  
Antisymmetric Tensor ◽  
Curved Spacetime ◽  
Antisymmetric Tensor Field ◽  
Rank 2 ◽  
Explicit Proof

We present an explicit proof that a minimal model of rank-2 antisymmetric field with spontaneous Lorentz violation and a classically equivalent vector field model are also quantum equivalent by calculating quantum effective actions of both theories. We comment on the issues encountered while checking quantum equivalence in curved spacetime.

scholarly journals REMARKS ON A CHERN–SIMONS-LIKE COUPLING

2011 ◽  
Vol 26 (37) ◽  
pp. 2813-2821
Author(s):  
PATRICIO GAETE
Keyword(s):  
Gauge Theory ◽  
Vector Field ◽  
Static Potential ◽  
Gauge Invariant ◽  
Massive Vector ◽  
Hidden Sector ◽  
Dependent Variables ◽  
Qualitative Nature ◽  
Path Dependent ◽  
Chern Simons

We consider the static quantum potential for a gauge theory which includes a light massive vector field interacting with the familiar U (1) QED photon via a Chern–Simons-like coupling, by using the gauge-invariant, but path-dependent, variables formalism. An exactly screening phase is then obtained, which displays a marked departure of a qualitative nature from massive axionic electrodynamics. The above static potential profile is similar to that encountered in axionic electrodynamics consisting of a massless axion-like field, as well as to that encountered in the coupling between the familiar U (1) QED photon and a second massive gauge field living in the so-called U (1)h hidden-sector, inside a superconducting box.

scholarly journals DUALITY INVARIANCE OF COSMOLOGICAL SOLUTIONS WITH TORSION

1999 ◽  
Vol 14 (31) ◽  
pp. 4953-4966 ◽  
Author(s):  
DEBASHIS GANGOPADHYAY ◽  
SOUMITRA SENGUPTA
Keyword(s):  
Physical Meaning ◽  
Tensor Field ◽  
Antisymmetric Tensor ◽  
Dilaton Field ◽  
Maximal Symmetry ◽  
Killing Vectors ◽  
Cosmological Solutions ◽  
Antisymmetric Tensor Field ◽  
Vacuum Solutions

We show that for a string moving in a background consisting of maximally symmetric gravity, dilaton field and second rank antisymmetric tensor field, the O(d) ⊗ O(d) transformation on the vacuum solutions gives inequivalent solutions that are not maximally symmetric. We then show that the usual physical meaning of maximal symmetry can be made to remain unaltered even if torsion is present and illustrate this through two toy models by determining the torsion fields, the metric and Killing vectors. Finally we show that under the O(d) ⊗ O(d) transformation this generalized maximal symmetry can be preserved under certain conditions. This is interesting in the context of string related cosmological backgrounds.

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