scholarly journals BRST analysis and BFV quantization of the generalized quantum rigid rotor

2021 ◽  
pp. 2150116
Author(s):  
Ronaldo Thibes
Keyword(s):  
Field Theory ◽  
Sigma Model ◽  
Brst Symmetry ◽  
Symmetry Analysis ◽  
Nonlinear Sigma Model ◽  
Canonical Structure ◽  
Rigid Rotor ◽  
Gauge Invariant ◽  
Gauge Fixing ◽  
Functional Quantization

We identify a strong similarity among several distinct originally second-class systems, including both mechanical and field theory models, which can be naturally described in a gauge-invariant way. The canonical structure of such related systems is encoded into a gauge-invariant generalization of the quantum rigid rotor. We perform the BRST symmetry analysis and the BFV functional quantization for the mentioned gauge-invariant version of the generalized quantum rigid rotor. We obtain different equivalent effective actions according to specific gauge-fixing choices, showing explicitly their BRST symmetries. We apply and exemplify the ideas discussed to two particular models, namely, motion along an elliptical path and the [Formula: see text] nonlinear sigma model, showing that our results reproduce and connect previously unrelated known gauge-invariant systems.

scholarly journals Symmetry restoration and the gluon mass in the Landau gauge

2021 ◽  
Vol 10 (2) ◽  
Author(s):  
Urko Reinosa ◽  
Julien Serreau ◽  
Rodrigo Carmo Terin ◽  
Matthieu Tissier
Keyword(s):  
Field Theory ◽  
Sigma Model ◽  
Landau Gauge ◽  
Two Dimensions ◽  
Nonlinear Sigma Model ◽  
Yang Mills ◽  
Local Field Theory ◽  
Gauge Fixing ◽  
Gribov Ambiguity ◽  
Gribov Copies

We investigate the generation of a gluon screening mass in Yang-Mills theory in the Landau gauge. We propose a gauge-fixing procedure where the Gribov ambiguity is overcome by summing over all Gribov copies with some weight function. This can be formulated in terms of a local field theory involving constrained, nonlinear sigma model fields. We show that a phenomenon of radiative symmetry restoration occurs in this theory, similar to what happens in the standard nonlinear sigma model in two dimensions. This results in a nonzero gluon screening mass, as seen in lattice simulations.

scholarly journals A master exceptional field theory

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
Guillaume Bossard ◽  
Axel Kleinschmidt ◽  
Ergin Sezgin
Keyword(s):  
Field Theory ◽  
Gauge Invariance ◽  
Sigma Model ◽  
Linear Equations ◽  
Field Theories ◽  
Gauge Invariant ◽  
Non Linear ◽  
Non Linear Equations

Abstract We construct a pseudo-Lagrangian that is invariant under rigid E11 and transforms as a density under E11 generalised diffeomorphisms. The gauge-invariance requires the use of a section condition studied in previous work on E11 exceptional field theory and the inclusion of constrained fields that transform in an indecomposable E11-representation together with the E11 coset fields. We show that, in combination with gauge-invariant and E11-invariant duality equations, this pseudo-Lagrangian reduces to the bosonic sector of non-linear eleven-dimensional supergravity for one choice of solution to the section condi- tion. For another choice, we reobtain the E8 exceptional field theory and conjecture that our pseudo-Lagrangian and duality equations produce all exceptional field theories with maximal supersymmetry in any dimension. We also describe how the theory entails non-linear equations for higher dual fields, including the dual graviton in eleven dimensions. Furthermore, we speculate on the relation to the E10 sigma model.

scholarly journals UNDERLYING GAUGE SYMMETRIES OF SECOND-CLASS CONSTRAINTS SYSTEMS

2007 ◽  
Vol 22 (04) ◽  
pp. 787-833 ◽  
Author(s):  
M. I. KRIVORUCHENKO ◽  
AMAND FAESSLER ◽  
A. A. RADUTA ◽  
C. FUCHS
Keyword(s):  
Nonlinear Sigma Model ◽  
Dimensional Sphere ◽  
Wigner Functions ◽  
Gauge Invariant ◽  
Gauge Transformations ◽  
Gauge Symmetries ◽  
Concrete Form ◽  
Gauge Fixing ◽  
General Velocity ◽  
Original Configuration

Gauge-invariant systems in unconstrained configuration and phase spaces, equivalent to second-class constraints systems upon a gauge-fixing, are discussed. A mathematical pendulum on an (n-1)-dimensional sphere Sn-1 as an example of a mechanical second-class constraints system and the O(n) nonlinear sigma model as an example of a field theory under second-class constraints are discussed in details and quantized using the existence of underlying dilatation gauge symmetry and by solving the constraint equations explicitly. The underlying gauge symmetries involve, in general, velocity dependent gauge transformations and new auxiliary variables in extended configuration space. Systems under second-class holonomic constraints have gauge-invariant counterparts within original configuration and phase spaces. The Dirac's supplementary conditions for wave functions of first-class constraints systems are formulated in terms of the Wigner functions which admit, as we show, a broad set of physically equivalent supplementary conditions. Their concrete form depends on the manner the Wigner functions are extrapolated from the constraint submanifolds into the whole phase space.

scholarly journals Universal Superspace Unitary Operator for Some Interesting Abelian Models: Superfield Approach

2016 ◽  
Vol 2016 ◽  
pp. 1-11 ◽  
Author(s):  
T. Bhanja ◽  
N. Srinivas ◽  
R. P. Malik
Keyword(s):  
Gauge Theories ◽  
Unitary Operator ◽  
Brst Symmetry ◽  
Scalar Fields ◽  
Gauge Field Theory ◽  
Rigid Rotor ◽  
Complex Scalar ◽  
Gauge Invariant ◽  
Hermitian Conjugate ◽  
Symmetry Transformations

Within the framework of augmented version of superfield formalism, we derive the superspace unitary operator and show its usefulness in the derivation of Becchi-Rouet-Stora-Tyutin (BRST) and anti-BRST symmetry transformations for a set of interesting models for the Abelian 1-form gauge theories. These models are (i) a one (0+1)-dimensional (1D) toy model of a rigid rotor, (ii) the two (1+1)-dimensional (2D) modified versions of the Proca and anomalous Abelian 1-form gauge theories, and (iii) the 2D self-dual bosonic gauge field theory. We provide, in some sense, the alternatives to the horizontality condition (HC) and the gauge invariant restrictions (GIRs) in the language of the above superspace (SUSP) unitary operator. One of the key observations of our present endeavor is the result that the SUSP unitary operator and its Hermitian conjugate are found to be thesameforallthe Abelian models under consideration (including the 4DinteractingAbelian 1-form gauge theories with Dirac and complex scalar fields which have been discussed earlier). Thus, we establish theuniversalityof the SUSP operator for the above Abelian theories.

scholarly journals NEW SPIN-2 GAUGED SIGMA MODELS AND GENERAL CONFORMAL FIELD THEORY

1998 ◽  
Vol 13 (26) ◽  
pp. 4487-4512 ◽  
Author(s):  
J. DE BOER ◽  
M. B. HALPERN
Keyword(s):  
Field Theory ◽  
Sigma Models ◽  
Large Class ◽  
Sigma Model ◽  
Field Theories ◽  
Nonlinear Sigma Model ◽  
Conformal Field Theories ◽  
Conformal Field ◽  
Local Gauge Symmetry ◽  
Action Formulation

Recently, we have studied the general Virasoro construction at one loop in the background of the general nonlinear sigma model. Here, we find the action formulation of these new conformal field theories when the background sigma model is itself conformal. In this case, the new conformal field theories are described by a large class of new spin-2 gauged sigma models. As examples of the new actions, we discuss the spin-2 gauged WZW actions, which describe the conformal field theories of the generic affine-Virasoro construction, and the spin-2 gauged g/h coset constructions. We are able to identify the latter as the actions of the local Lie h-invariant conformal field theories, a large class of generically irrational conformal field theories with a local gauge symmetry.

scholarly journals QUANTUM AND CLASSICAL GAUGE SYMMETRIES IN A MODIFIED QUANTIZATION SCHEME

2001 ◽  
Vol 16 (10) ◽  
pp. 1775-1788 ◽  
Author(s):  
KAZUO FUJIKAWA ◽  
HIROAKI TERASHIMA
Keyword(s):  
Gauge Symmetry ◽  
Brst Symmetry ◽  
Mass Term ◽  
Large Mass ◽  
Quantization Scheme ◽  
Mass Limit ◽  
Classical Action ◽  
Gauge Invariant ◽  
Gauge Fixing ◽  
Nonlinear Gauge

The use of the mass term as a gauge fixing term has been studied by Zwanziger, Parrinello and Jona-Lasinio, which is related to the nonlinear gauge [Formula: see text] of Dirac and Nambu in the large mass limit. We have recently shown that this modified quantization scheme is in fact identical to the conventional local Faddeev–Popov formula without taking the large mass limit, if one takes into account the variation of the gauge field along the entire gauge orbit and if the Gribov complications can be ignored. This suggests that the classical massive vector theory, for example, is interpreted in a more flexible manner either as a gauge invariant theory with a gauge fixing term added, or as a conventional massive nongauge theory. As for massive gauge particles, the Higgs mechanics, where the mass term is gauge-invariant, has a more intrinsic meaning. It is suggested that we extend the notion of quantum gauge symmetry (BRST symmetry) not only to classical gauge theory but also to a wider class of theories whose gauge symmetry is broken by some extra terms in the classical action. We comment on the implications of this extended notion of quantum gauge symmetry.

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