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 Superfield approach to nilpotent symmetries in 3D Jackiw–Pi model of massive non-Abelian theory

2014 ◽  
Vol 92 (9) ◽  
pp. 1033-1042 ◽  
Author(s):  
S. Gupta ◽  
R. Kumar ◽  
R.P. Malik
Keyword(s):  
Gauge Theory ◽  
Brst Symmetry ◽  
Point Of View ◽  
Abelian Gauge ◽  
Gauge Invariant ◽  
Abelian Gauge Theory ◽  
Gauge Transformations ◽  
Yang Mills ◽  
Symmetry Transformations ◽  
Augmented Superfield Formalism

In the available literature, only the Becchi–Rouet–Stora–Tyutin (BRST) symmetries are known for the Jackiw–Pi model of the three (2 + 1)-dimensional (3D) massive non-Abelian gauge theory. We derive the off-shell nilpotent [Formula: see text] and absolutely anticommuting (sbsab + sabsb = 0) (anti-)BRST transformations s(a)b corresponding to the usual Yang–Mills gauge transformations of this model by exploiting the “augmented” superfield formalism where the horizontality condition and gauge invariant restrictions blend together in a meaningful manner. There is a non-Yang–Mills (NYM) symmetry in this theory, too. However, we do not touch the NYM symmetry in our present endeavor. This superfield formalism leads to the derivation of an (anti-)BRST invariant Curci–Ferrari restriction, which plays a key role in the proof of absolute anticommutativity of s(a)b. The derivation of the proper anti-BRST symmetry transformations is important from the point of view of geometrical objects called gerbes. A novel feature of our present investigation is the derivation of the (anti-)BRST transformations for the auxiliary field ρ from our superfield formalism, which is neither generated by the (anti-)BRST charges nor obtained from the requirements of nilpotency and (or) absolute anticommutativity of the (anti-)BRST symmetries for our present 3D non-Abelian 1-form gauge theory.

scholarly journals NON-ABELIAN GAUGE THEORIES AS A CONSEQUENCE OF PERTURBATIVE QUANTUM GAUGE INVARIANCE

1999 ◽  
Vol 14 (21) ◽  
pp. 3421-3432 ◽  
Author(s):  
A. ASTE ◽  
G. SCHARF
Keyword(s):  
Gauge Theory ◽  
Gauge Invariance ◽  
Gauge Theories ◽  
Fundamental Concept ◽  
Abelian Gauge ◽  
Abelian Gauge Theory ◽  
Yang Mills ◽  
Vector Bosons ◽  
Perturbative Quantum

We show for the case of interacting massless vector bosons, how the structure of Yang–Mills theories emerges automatically from a more fundamental concept, namely perturbative quantum gauge invariance. It turns out that the coupling in a non-Abelian gauge theory is necessarily of Yang–Mills type plus divergence- and coboundary-couplings. The extension of the method to massive gauge theories is briefly discussed.

scholarly journals STRING HAMILTONIAN FROM GENERALIZED YANG–MILLS GAUGE THEORY IN TWO DIMENSIONS

2004 ◽  
Vol 19 (02) ◽  
pp. 205-225 ◽  
Author(s):  
FLORIAN DUBATH ◽  
SIMONE LELLI ◽  
ANNA RISSONE
Keyword(s):  
Gauge Theory ◽  
String Theory ◽  
Space Time ◽  
Two Dimensions ◽  
Two Dimensional ◽  
Bosonic Field ◽  
Standard Case ◽  
Free Fermions ◽  
Yang Mills ◽  
Large N

Two-dimensional SU (N) Yang–Mills theory is known to be equivalent to a string theory, as found by Gross in the large N limit, using the 1/N expansion. Later it was found that even a generalized YM theory leads to a string theory of the Gross type. In the standard YM theory case, Douglas and others found the string Hamiltonian describing the propagation and the interactions of states made of strings winding on a cylindrical space–time. We address the problem of finding a similar Hamiltonian for the generalized YM theory. As in the standard case we start by writing the theory as a theory of free fermions. Performing a bosonization, we express the Hamiltonian in terms of the modes of a bosonic field, that are interpreted as in the standard case as creation and destruction operators for states of strings winding around the cylindrical space–time. The result is similar to the standard Hamiltonian, but with new kinds of interaction vertices.

Higher spin theories in flat space–time

2018 ◽  
Vol 33 (34) ◽  
pp. 1845007
Author(s):  
Loriano Bonora
Keyword(s):  
Equations Of Motion ◽  
Flat Space ◽  
Space Time ◽  
Local Fields ◽  
Field Theories ◽  
Gauge Transformations ◽  
Yang Mills ◽  
Higher Spin ◽  
Chern Simons

It is shown that, contrary to a widespread prejudice, massless higher spin (HS) field theories can be defined in flat space–time. Examples of Yang–Mills-like theories with infinite many local fields of any spin are constructed explicitly in any dimension, along with Chern–Simons-like models in any odd dimension. These theories are defined via actions invariant under HS gauge transformations and their equations of motion are derived. It is also briefly explained why these theories circumvent well-known no-go theorems.

scholarly journals INTERSECTION OF YANG–MILLS THEORY WITH GAUGE DESCRIPTION OF GENERAL RELATIVITY

2012 ◽  
Vol 27 (20) ◽  
pp. 1250108
Author(s):  
MARTIN KOBER
Keyword(s):  
General Relativity ◽  
Field Strength ◽  
Gauge Group ◽  
Additional Term ◽  
Interaction Structure ◽  
Gauge Invariant ◽  
Gauge Transformations ◽  
Yang Mills ◽  
Commutation Relations ◽  
Strength Tensor

An intersection of Yang–Mills theory with the gauge description of general relativity is considered. This intersection has its origin in a generalized algebra, where the generators of the SO(3, 1) group as gauge group of general relativity and the generators of a SU(N) group as gauge group of Yang–Mills theory are not separated anymore but are related by fulfilling nontrivial commutation relations with each other. Because of the Coleman–Mandula theorem this algebra cannot be postulated as Lie algebra. As consequence, extended gauge transformations as well as an extended expression for the field strength tensor is obtained, which contains a term consisting of products of the Yang–Mills connection and the connection of general relativity. Accordingly a new gauge invariant action incorporating the additional term of the generalized field strength tensor is built, which depends of course on the corresponding tensor determining the additional intersection commutation relations. This means that the theory describes a decisively modified interaction structure between the Yang–Mills gauge field and the gravitational field leading to a violation of the equivalence principle.

scholarly journals THE BV MASTER EQUATION FOR THE WILSON ACTION IN GENERAL YANG-MILLS GAUGE THEORY

2008 ◽  
Vol 23 (14n15) ◽  
pp. 2255-2256
Author(s):  
TAKESHI HIGASHI ◽  
ETSUKO ITOU ◽  
TAICHIRO KUGO
Keyword(s):  
Renormalization Group ◽  
Gauge Theory ◽  
Master Equation ◽  
Effective Action ◽  
Gauge Invariance ◽  
Abelian Gauge ◽  
Abelian Gauge Theory ◽  
Yang Mills ◽  
Usual Form

We study the four dimensional gauge theory within Wilsonian Renormalization Group (WRG) method. The Wilson effective action for general Yang-Mills gauge theory is shown to satisfy the usual form of Batalin-Vilkovisky (BV) master equation, despite that a momentum cutoff apparently breaks the gauge invariance. In the case of Abelian gauge theory, in particular, it actually deduces the Ward-Takahashi identity for Wilson action recently derived by Sonoda. We elucidated the relation of our Wilson master action with that derived by Ref. 2 and, in particular, showed that our BV Master equation really reproduced the Sonoda's WT identity for the Wilson action in QED. (This is a proceeding to the conference based on the poster given by E.I.).

scholarly journals SYMMETRIES OF p-BRANES

1993 ◽  
Vol 08 (30) ◽  
pp. 5367-5381 ◽  
Author(s):  
R. PERCACCI ◽  
E. SEZGIN
Keyword(s):  
Global Symmetries ◽  
Sigma Model ◽  
Space Time ◽  
Gauge Transformations ◽  
Yang Mills ◽  
Infinite Dimensional ◽  
Invariance Properties ◽  
Group Manifold ◽  
Mills Field

Using canonical methods, we study the invariance properties of a bosonic p-brane propagating in a curved background locally diffeomorphic to M×G, where M is space-time and G a group manifold. The action is that of a gauged sigma model in p+1 dimensions coupled to a Yang-Mills field and a (p+1) form in M. We construct the generators of Yang-Mills and tensor gauge transformations and exhibit the role of the (p+1) form in canceling the potential Schwinger terms. We also discuss the Noether currents associated with the global symmetries of the action and the question of the existence of infinite-dimensional symmetry algebras, analogous to the Kac-Moody symmetry of the string.

YANG–MILLS THEORY AND NON-LOCAL REGULARIZATION

1991 ◽  
Vol 06 (17) ◽  
pp. 1581-1587 ◽  
Author(s):  
J. W. MOFFAT ◽  
S. M. ROBBINS
Keyword(s):  
Gauge Theory ◽  
Gauge Invariance ◽  
Abelian Gauge ◽  
Abelian Gauge Theory ◽  
Yang Mills ◽  
Local Regularization ◽  
Non Local

The lowest order diagrams required to guarantee decoupling and gauge invariance in non-local regularized, non-Abelian gauge theory are derived.

scholarly journals A PEDAGOGICAL INTRODUCTION TO THE SLAVNOV FORMULATION OF QUANTUM YANG–MILLS THEORY

2011 ◽  
Vol 08 (04) ◽  
pp. 821-834
Author(s):  
HOSSEIN GHORBANI ◽  
GIAMPIERO ESPOSITO
Keyword(s):  
Quantum Gravity ◽  
Gauge Invariance ◽  
Lorentz Invariance ◽  
Functional Integral ◽  
Coulomb Gauge ◽  
Gauge Transformations ◽  
Yang Mills ◽  
S Matrix ◽  
Ghost Field

Over the last few years, Slavnov has proposed a formulation of quantum Yang–Mills theory in the Coulomb gauge which preserves simultaneously manifest Lorentz invariance and gauge invariance of the ghost field Lagrangian. This paper presents in detail some of the necessary calculations, i.e. those dealing with the functional integral for the S-matrix and its invariance under shifted gauge transformations. The extension of this formalism to quantum gravity in the Prentki gauge deserves consideration.

Yang–Mills theory in the SO(2,3)⋆ model of noncommutative gravity

2018 ◽  
Vol 33 (34) ◽  
pp. 1845005
Author(s):  
Marija Dimitrijević-Ćirić ◽  
Dragoljub Gočanin ◽  
Nikola Konjik ◽  
Voja Radovanović
Keyword(s):  
Quark Gluon Plasma ◽  
Flat Space ◽  
Gluon Plasma ◽  
Big Bang ◽  
Space Time ◽  
Noncommutative Space ◽  
Theoretical Treatment ◽  
Gauge Transformations ◽  
Yang Mills ◽  
Noncommutative Gravity

According to the standard cosmological model, thermodynamic conditions of the early Universe were such that nuclear matter existed in the state of quark–gluon plasma, rather than hadrons. On the other hand, it is generally believed that quantum gravity effects become ever more stronger as we approach the Big Bang, in particular, we expect that the phenomenon of space–time noncommutativity will be significant. Thus we are led to consider the properties of quarks and gluons in noncommutative space–time. For this, we employ the [Formula: see text] model of noncommutative gravity. As a first step towards the full theoretical treatment of the effects of noncommutativity on quark–gluon plasma, our main goal in this paper is to consistently incorporate Yang–Mills gauge fields in the [Formula: see text] framework and investigate their coupling to gravity that arises due to space–time noncommutativity. We construct an action that is invariant under deformed [Formula: see text] gauge transformations and expand it perturbatively in orders of the canonical deformation parameter [Formula: see text] via Seiberg–Witten map. In particular, we analyze the flat-space–time limit and demonstrate that residual noncommutativity induces various new couplings of quarks and gluons.

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