scholarly journals Poisson gauge theory

2021 ◽  
Vol 2021 (9) ◽  
Author(s):  
Vladislav G. Kupriyanov
Keyword(s):  
Gauge Theory ◽  
Field Strength ◽  
Matter Field ◽  
Field Equations ◽  
Gauge Transformations ◽  
Gauge Algebra ◽  
Gauge Symmetries ◽  
Covariant Derivatives ◽  
Proposed Model ◽  
Poisson Field

Abstract The Poisson gauge algebra is a semi-classical limit of complete non- commutative gauge algebra. In the present work we formulate the Poisson gauge theory which is a dynamical field theoretical model having the Poisson gauge algebra as a corresponding algebra of gauge symmetries. The proposed model is designed to investigate the semi-classical features of the full non-commutative gauge theory with coordinate dependent non-commutativity Θab(x), especially whose with a non-constant rank. We derive the expression for the covariant derivative of matter field. The commutator relation for the covariant derivatives defines the Poisson field strength which is covariant under the Poisson gauge transformations and reproduces the standard U(1) field strength in the commutative limit. We derive the corresponding Bianchi identities. The field equations for the gauge and the matter fields are obtained from the gauge invariant action. We consider different examples of linear in coordinates Poisson structures Θab(x), as well as non-linear ones, and obtain explicit expressions for all proposed constructions. Our model is unique up to invertible field redefinitions and coordinate transformations.

A gauge theory of the Weyl group

1974 ◽  
Vol 340 (1622) ◽  
pp. 249-262 ◽  
Keyword(s):  
Field Theory ◽  
Gauge Theory ◽  
Conservation Laws ◽  
Weyl Group ◽  
Lorentz Group ◽  
Space Time ◽  
Gauge Fields ◽  
Field Equations ◽  
Covariant Derivatives ◽  
The World

The construction of field theory which exhibits invariance under the Weyl group with parameters dependent on space–time is discussed. The method is that used by Utiyama for the Lorentz group and by Kibble for the Poincaré group. The need to construct world-covariant derivatives necessitates the introduction of three sets of gauge fields which provide a local affine connexion and a vierbein system. The geometrical implications are explored; the world geometry has an affine connexion which is not symmetric but is semi-metric. A possible choice of Lagrangian for the gauge fields is presented, and the resulting field equations and conservation laws discussed.

scholarly journals TOPOLOGICALLY MASSIVE NON-ABELIAN THEORY: SUPERFIELD APPROACH

2011 ◽  
Vol 26 (25) ◽  
pp. 4419-4450 ◽  
Author(s):  
S. KRISHNA ◽  
A. SHUKLA ◽  
R. P. MALIK
Keyword(s):  
Gauge Theory ◽  
Gauge Symmetry ◽  
Brst Symmetry ◽  
Gauge Transformations ◽  
Abelian Theory ◽  
Gauge Symmetries ◽  
Vector Gauge ◽  
Symmetry Transformations ◽  
Brst Invariance ◽  
Lagrangian Densities

We apply the well-established techniques of geometrical superfield approach to Becchi–Rouet–Stora–Tyutin (BRST) formalism in the context of four (3+1)-dimensional (4D) dynamical non-Abelian 2-form gauge theory by exploiting its inherent "scalar" and "vector" gauge symmetry transformations and derive the corresponding off-shell nilpotent and absolutely anticommuting BRST and anti-BRST symmetry transformations. Our approach leads to the derivation of three (anti-)BRST invariant Curci–Ferrari (CF)-type restrictions that are found to be responsible for the absolute anticommutativity of the BRST and anti-BRST symmetry transformations. We derive the coupled Lagrangian densities that respect the (anti-)BRST symmetry transformations corresponding to the "vector" gauge transformations. We also capture the (anti-)BRST invariance of the CF-type restrictions and coupled Lagrangian densities within the framework of our superfield approach. We obtain, furthermore, the off-shell nilpotent (anti-)BRST symmetry transformations when the (anti-)BRST symmetry transformations corresponding to the "scalar" and "vector" gauge symmetries are merged together. These off-shell nilpotent "merged" (anti-)BRST symmetry transformations are, however, found to be non-anticommuting in nature.

scholarly journals Symplectic embeddings, homotopy algebras and almost Poisson gauge symmetry

2021 ◽  
Author(s):  
Vladislav G Kupriyanov ◽  
Richard J Szabo
Keyword(s):  
Gauge Theories ◽  
Differential Forms ◽  
Poisson Manifold ◽  
New Approach ◽  
Gauge Sector ◽  
Gauge Transformations ◽  
Gauge Algebra ◽  
Gauge Symmetries ◽  
Noncommutative Gauge Theories ◽  
Differential Graded Poisson Algebras

Abstract We formulate general definitions of semi-classical gauge transformations for noncommutative gauge theories in general backgrounds of string theory, and give novel explicit constructions using techniques based on symplectic embeddings of almost Poisson structures. In the absence of fluxes the gauge symmetries close a Poisson gauge algebra and their action is governed by a $P_\infty$-algebra which we construct explicitly from the symplectic embedding. In curved backgrounds they close a field dependent gauge algebra governed by an $L_\infty$-algebra which is not a $P_\infty$-algebra. Our technique produces new all orders constructions which are significantly simpler compared to previous approaches, and we illustrate its applicability in several examples of interest in noncommutative field theory and gravity. We further show that our symplectic embeddings naturally define a $P_\infty$-structure on the exterior algebra of differential forms on a generic almost Poisson manifold, which generalizes earlier constructions of differential graded Poisson algebras, and suggests a new approach to defining noncommutative gauge theories beyond the gauge sector and the semi-classical limit based on $A_\infty$-algebras.

scholarly journals NON-ABELIAN GAUGE SYMMETRIES INDUCED BY THE UNOBSERVABILITY OF EXTRA DIMENSIONS IN A KALUZA–KLEIN APPROACH

2006 ◽  
Vol 21 (03) ◽  
pp. 265-274 ◽  
Author(s):  
FRANCESCO CIANFRANI ◽  
GIOVANNI MONTANI
Keyword(s):  
Extra Dimensions ◽  
Gauge Coupling ◽  
Einstein Equations ◽  
Field Equations ◽  
Abelian Gauge ◽  
Gauge Transformations ◽  
Yang Mills ◽  
Gauge Symmetries ◽  
The Right ◽  
Kaluza Klein

In this work we deal with the extension of the Kaluza–Klein approach to a non-Abelian gauge theory; we show how we need to consider the link between the n-dimensional model and a four-dimensional observer physics, in order to reproduce field equations and gauge transformations in the four-dimensional picture. More precisely, in field equations any dependence on extra coordinates is canceled out by an integration, as consequence of the unobservability of extra dimensions. Thus, by virtue of this extra dimension unobservability, we are able to recast the multidimensional Einstein equations into the four-dimensional Einstein–Yang–Mills ones, as well as all the right gauge transformations of fields are induced. The same analysis is performed for the Dirac equation describing the dynamics of the matter fields and, again, the gauge coupling with Yang–Mills fields are inferred from the multidimensional free fields theory, together with the proper spinors transformations.

scholarly journals DIAGRAMMATICS OF BRAIDED GROUP GAUGE THEORY

1999 ◽  
Vol 08 (06) ◽  
pp. 731-771 ◽  
Author(s):  
SHAHN MAJID
Keyword(s):  
Gauge Theory ◽  
Local Structure ◽  
Fiber Bundles ◽  
Principal Bundles ◽  
Braided Group ◽  
Gauge Transformations ◽  
Covariant Derivatives ◽  
Global Gauge

We develop a gauge theory or theory of bundles and connections on them at the level of braids and tangles. Extending recent algebraic work, we provide now a fully diagrammatic treatment of principal bundles, a theory of global gauge transformations, associated braided fiber bundles and covariant derivatives on them. We describe the local structure for a concrete ℤ3-graded or 'anyonic' realization of the theory.

scholarly journals κ-Minkowski-deformation of U(1) gauge theory

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
V. G. Kupriyanov ◽  
M. Kurkov ◽  
P. Vitale
Keyword(s):  
Gauge Theory ◽  
Field Strength ◽  
Gauge Invariance ◽  
Physical Meaning ◽  
Space Time ◽  
Action Functional ◽  
Gauge Transformations ◽  
Yang Mills ◽  
Integration Measure

Abstract We construct a noncommutative kappa-Minkowski deformation of U(1) gauge theory, following a general approach, recently proposed in JHEP 08 (2020) 041. We obtain an exact (all orders in the non-commutativity parameter) expression for both the deformed gauge transformations and the deformed field strength, which is covariant under these transformations. The corresponding Yang-Mills Lagrangian is gauge covariant and reproduces the Maxwell Lagrangian in the commutative limit. Gauge invariance of the action functional requires a non-trivial integration measure which, in the commutative limit, does not reduce to the trivial one. We discuss the physical meaning of such a nontrivial commutative limit, relating it to a nontrivial space-time curvature of the undeformed theory. Moreover, we propose a rescaled kappa-Minkowski noncommutative structure, which exhibits a standard flat commutative limit.

scholarly journals Four-dimensional noncommutative deformations of U(1) gauge theory and L∞ bootstrap.

2022 ◽  
Vol 2022 (1) ◽  
Author(s):  
Maxim Kurkov ◽  
Patrizia Vitale
Keyword(s):  
Gauge Theory ◽  
Field Strength ◽  
Gauge Theories ◽  
General Scheme ◽  
Three Dimensional ◽  
Theoretical Models ◽  
Classical Action ◽  
Gauge Transformations ◽  
Noncommutative Algebras ◽  
Noncommutative Gauge Theories

Abstract We construct a family of four-dimensional noncommutative deformations of U(1) gauge theory following a general scheme, recently proposed in JHEP 08 (2020) 041 for a class of coordinate-dependent noncommutative algebras. This class includes the $$ \mathfrak{su} $$ su (2), the $$ \mathfrak{su} $$ su (1, 1) and the angular (or λ-Minkowski) noncommutative structures. We find that the presence of a fourth, commutative coordinate x0 leads to substantial novelties in the expression for the deformed field strength with respect to the corresponding three-dimensional case. The constructed field theoretical models are Poisson gauge theories, which correspond to the semi-classical limit of fully noncommutative gauge theories. Our expressions for the deformed gauge transformations, the deformed field strength and the deformed classical action exhibit flat commutative limits and they are exact in the sense that all orders in the deformation parameter are present. We review the connection of the formalism with the L∞ bootstrap and with symplectic embeddings, and derive the L∞-algebra, which underlies our model.

scholarly journals Flavor symmetry of 5d SCFTs. Part II. Applications

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Lakshya Bhardwaj
Keyword(s):  
Gauge Theory ◽  
Flavor Symmetry ◽  
Gauge Algebra ◽  
Mass Deformation ◽  
General Method

Abstract In Part I of this series of papers, we described a general method for determining the flavor symmetry of any 5d SCFT which can be constructed by integrating out BPS particles from some 6d SCFT compactified on a circle. In this part, we apply the method to explicitly determine the flavor symmetry of those 5d SCFTs which reduce, upon a mass deformation, to some 5d$$ \mathcal{N} $$ N = 1 gauge theory carrying a simple gauge algebra. In these cases, the flavor symmetry of the 5d gauge theory is often enhanced at the conformal point. We use our method to determine this enhancement.

scholarly journals HAMILTONIAN COHOMOLOGICAL DERIVATION OF FOUR-DIMENSIONAL NONLINEAR GAUGE THEORIES

2002 ◽  
Vol 17 (16) ◽  
pp. 2191-2210 ◽  
Author(s):  
C. BIZDADEA ◽  
E. M. CIOROIANU ◽  
S. O. SALIU
Keyword(s):  
Gauge Theory ◽  
Gauge Theories ◽  
Scalar Fields ◽  
Gauge Algebra ◽  
Brst Cohomology ◽  
Nonlinear Gauge

Consistent couplings among a set of scalar fields, two types of one-forms and a system of two-forms are investigated in the light of the Hamiltonian BRST cohomology, giving a four-dimensional nonlinear gauge theory. The emerging interactions deform the first-class constraints, the Hamiltonian gauge algebra, as well as the reducibility relations.

DESITTER GAUGE THEORY OF GRAVITATION

2003 ◽  
Vol 14 (01) ◽  
pp. 41-48 ◽  
Author(s):  
G. ZET ◽  
V. MANTA ◽  
S. BABETI
Keyword(s):  
Gauge Theory ◽  
Riemann Tensor ◽  
Space Time ◽  
Point Of View ◽  
Field Equations ◽  
Minkowski Space Time ◽  
Strength Tensor ◽  
Group A ◽  
Theory Of Gravitation ◽  
Tensor Formula

A deSitter gauge theory of gravitation over a spherical symmetric Minkowski space–time is developed. The "passive" point of view is adapted, i.e., the space–time coordinates are not affected by group transformations; only the fields change under the action of the symmetry group. A particular ansatz for the gauge fields is chosen and the components of the strength tensor are computed. An analytical solution of Schwarzschild–deSitter type is obtained in the case of null torsion. It is concluded that the deSitter group can be considered as a "passive" gauge symmetry for gravitation. Because of their complexity, all the calculations, inclusive of the integration of the field equations, are performed using an analytical program conceived in GRTensorII for MapleV. The program allows one to compute (without using a metric) the strength tensor [Formula: see text], Riemann tensor [Formula: see text], Ricci tensor [Formula: see text], curvature scalar [Formula: see text], field equations, and the integration of these equations.

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