scholarly journals A NOVEL OBSERVATION IN THE BRST APPROACH TO A FREE SPINNING RELATIVISTIC PARTICLE

2013 ◽  
Vol 28 (21) ◽  
pp. 1350108
Author(s):  
S. KRISHNA ◽  
D. SHUKLA ◽  
R. P. MALIK
Keyword(s):  
Physical State ◽  
Gauge Theories ◽  
Relativistic Particle ◽  
Continuous Symmetry ◽  
Conserved Charges ◽  
Symmetry Operators ◽  
Symmetry Transformations

For the newly proposed coupled (but equivalent) Lagrangians for the supersymmetric (SUSY) system of a one (0+1)-dimensional spinning relativistic particle, we derive the Noether conserved charges corresponding to its (super)gauge, Becchi–Rouet–Stora–Tyutin (BRST), anti-BRST and ghost-scale symmetry transformations. We deduce the underlying algebra amongst the continuous symmetry operators and corresponding conserved charges. We point out a novel observation that emerges, for this specific SUSY system, when we discuss it within the framework of BRST formalism. In particular, the requirement of the physicality criteria with the (anti-)BRST charges leads to a completely new observation because, as it turns out, one of the primary constraints does not annihilate the physical state of the theory. We have never come across this kind of result in the realm of BRST approach to usual gauge theories. We provide the physical and theoretical reasons behind the above observation.

scholarly journals Nilpotent (anti-)BRST and (anti-)co-BRST symmetries in 2D non-Abelian gauge theory: Some novel observations

2021 ◽  
Author(s):  
S. Kumar ◽  
B. K. Kureel ◽  
R. P. Malik
Keyword(s):  
Differential Geometry ◽  
Gauge Theory ◽  
Brst Symmetry ◽  
Abelian Gauge ◽  
Abelian Gauge Theory ◽  
Conserved Charges ◽  
Symmetry Operators ◽  
Symmetry Transformations ◽  
Continuous Symmetries ◽  
Lagrangian Densities

We discuss the nilpotent Becchi–Rouet–Stora–Tyutin (BRST), anti-BRST and (anti-)co-BRST symmetry transformations and derive their corresponding conserved charges in the case of a two (1[Formula: see text]+[Formula: see text]1)-dimensional (2D) self-interacting non-Abelian gauge theory (without any interaction with matter fields). We point out a set of novel features that emerge out in the BRST and co-BRST analysis of the above 2D gauge theory. The algebraic structures of the symmetry operators (and corresponding conserved charges) and their relationship with the cohomological operators of differential geometry are established too. To be more precise, we demonstrate the existence of a single Lagrangian density that respects the continuous symmetries which obey proper algebraic structure of the cohomological operators of differential geometry. In the literature, such observations have been made for the coupled (but equivalent) Lagrangian densities of the 4D non-Abelian gauge theory. We lay emphasis on the existence and properties of the Curci–Ferrari (CF)-type restrictions in the context of (anti-)BRST and (anti-)co-BRST symmetry transformations and pinpoint their key differences and similarities. All the observations, connected with the (anti-)co-BRST symmetries, are completely novel.

scholarly journals Abelian p-form (p = 1, 2, 3) gauge theories as the field theoretic models for the Hodge theory

2014 ◽  
Vol 29 (24) ◽  
pp. 1450135 ◽  
Author(s):  
R. Kumar ◽  
S. Krishna ◽  
A. Shukla ◽  
R. P. Malik
Keyword(s):  
Gauge Theory ◽  
Gauge Theories ◽  
Hodge Theory ◽  
Space Time ◽  
Continuous Symmetry ◽  
Gauge Transformations ◽  
Perfect Model ◽  
De Rham ◽  
Symmetry Transformations ◽  
Dimensions Of Space

Taking the simple examples of an Abelian 1-form gauge theory in two (1+1)-dimensions, a 2-form gauge theory in four (3+1)-dimensions and a 3-form gauge theory in six (5+1)-dimensions of space–time, we establish that such gauge theories respect, in addition to the gauge symmetry transformations that are generated by the first-class constraints of the theory, additional continuous symmetry transformations. We christen the latter symmetry transformations as the dual-gauge transformations. We generalize the above gauge and dual-gauge transformations to obtain the proper (anti-)BRST and (anti-)dual-BRST transformations for the Abelian 3-form gauge theory within the framework of BRST formalism. We concisely mention such symmetries for the 2D free Abelian 1-form and 4D free Abelian 2-form gauge theories and briefly discuss their topological aspects in our present endeavor. We conjecture that any arbitrary Abelian p-form gauge theory would respect the above cited additional symmetry in D = 2p(p = 1, 2, 3, …) dimensions of space–time. By exploiting the above inputs, we establish that the Abelian 3-form gauge theory, in six (5+1)-dimensions of space–time, is a perfect model for the Hodge theory whose discrete and continuous symmetry transformations provide the physical realizations of all aspects of the de Rham cohomological operators of differential geometry. As far as the physical utility of the above nilpotent symmetries is concerned, we demonstrate that the 2D Abelian 1-form gauge theory is a perfect model of a new class of topological theory and 4D Abelian 2-form as well as 6D Abelian 3-form gauge theories are the field theoretic models for the quasi-topological field theory.

SUPERSYMMETRIC TENSOR GAUGE THEORIES

1989 ◽  
Vol 04 (14) ◽  
pp. 1343-1353 ◽  
Author(s):  
T.E. CLARK ◽  
C.-H. LEE ◽  
S.T. LOVE
Keyword(s):  
Gauge Theory ◽  
Gauge Symmetry ◽  
Sigma Models ◽  
Gauge Field ◽  
Gauge Theories ◽  
Symmetric Tensor ◽  
Global Symmetry ◽  
Invariant Action ◽  
Symmetry Transformations ◽  
Linear Sigma Models

The supersymmetric extensions of anti-symmetric tensor gauge theories and their associated tensor gauge symmetry transformations are constructed. The classical equivalence between such supersymmetric tensor gauge theories and supersymmetric non-linear sigma models is established. The global symmetry of the supersymmetric tensor gauge theory is gauged and the locally invariant action is obtained. The supercurrent on the Kähler manifold is found in terms of the supersymmetric tensor gauge field.

scholarly journals THE RELATIONS BETWEEN GENERALIZED FIELDS AND SUPERFIELDS FORMALISMS OF THE BATALIN–VILKOVISKY METHOD OF QUANTIZATION

2004 ◽  
Vol 19 (14) ◽  
pp. 2339-2353 ◽  
Author(s):  
ÖMER F. DAYI
Keyword(s):  
General Solution ◽  
Master Equation ◽  
Gauge Theories ◽  
Relativistic Particle ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Yang Mills ◽  
Topological Quantum ◽  
Topological Quantum Field Theories

A general solution of the Batalin–Vilkovisky master equation was formulated in terms of generalized fields. Recently, a superfields approach of obtaining solutions of the Batalin–Vilkovisky master equation is also established. Superfields formalism is usually applied to topological quantum field theories. However, generalized fields method is suitable to find solutions of the Batalin–Vilkovisky master equation either for topological quantum field theories or the usual gauge theories like Yang–Mills theory. We show that by truncating some components of superfields with appropriate actions, generalized fields formalism of the usual gauge theories result. We demonstrate that for some topological quantum field theories and the relativistic particle both of the methods possess the same field contents and yield similar results. Inspired by the observed relations, we give the solution of the BV master equation for on-shell N=1 supersymmetric Yang–Mills theory utilizing superfields.

scholarly journals Gauge-independent Theory of Symmetry. I.

1964 ◽  
Vol 17 (4) ◽  
pp. 431 ◽  
Author(s):  
LJ Tassie ◽  
HA Buchdahl
Keyword(s):  
Electromagnetic Field ◽  
Single Particle ◽  
Equations Of Motion ◽  
Classical Mechanics ◽  
Conserved Quantities ◽  
Continuous Symmetry ◽  
Symmetry Properties ◽  
Symmetry Transformations ◽  
Hamiltonian Forms

The invariance of a system under a given transformation of coordinates is usually taken to mean that its Lagrangian is invariant under that transformation. Consequently, whether or not the system is invariant will depend on the gauge used in describing the system. By defining invariance of a system to mean the invariance of its equations of motion, a gauge-independent theory of symmetry properties is obtained for classical mechanics in both the Lagrangian and Hamiltonian forms. The conserved quantities associated with continuous symmetry transformations are obtained. The system of a single particle moving in a given electromagnetic field is considered in detail for various symmetries of the electromagnetic field, and the appropriate conserved quantities are found.

scholarly journals R Symmetry and the Topological Twist of N = 2 Effective Supergravities of Heterotic Strings

1997 ◽  
Vol 12 (02) ◽  
pp. 379-418 ◽  
Author(s):  
Marco Billó ◽  
Pietro Fré ◽  
Riccardo D'auria ◽  
Sergio Ferrara ◽  
Paolo Soriani ◽  
...  
Keyword(s):  
Gauge Theories ◽  
The Other ◽  
Tree Level ◽  
Vector Multiplet ◽  
Continuous Symmetry ◽  
Yang Mills ◽  
Heterotic Strings ◽  
Axion Field ◽  
Effective Theories ◽  
R Symmetry

We discuss R symmetries in locally supersymmetric N = 2 gauge theories coupled to hypermultiplets which can be thought of as effective theories of heterotic superstring models. In this type of supergravities a suitable R symmetry exists and can be used to topologically twist the theory: the vector multiplet containing the dilaton–axion field has different R charge assignments with respect to the other vector multiplets. Correspondingly a system of coupled instanton equations emerges, mixing gravitational and Yang–Mills instantons with triholomorphic hyperinstantons and axion instantons. For the tree level classical special manifolds ST(n) = SU(1,1)/U(1) × SO(2,n)/[SO(2) × SO(n)], R symmetry with the specified properties is a continuous symmetry, but for the quantum-corrected manifolds [Formula: see text] a discrete R group of electric–magnetic duality rotations is sufficient and we argue that it exists.

scholarly journals Nilpotent and absolutely anticommuting symmetries in the Freedman–Townsend model: Augmented superfield formalism

2014 ◽  
Vol 29 (31) ◽  
pp. 1450183 ◽  
Author(s):  
A. Shukla ◽  
S. Krishna ◽  
R. P. Malik
Keyword(s):  
Gauge Theories ◽  
Brst Symmetry ◽  
Kinetic Term ◽  
The Novel ◽  
Gauge Invariant ◽  
Yang Mills ◽  
Gauge Symmetries ◽  
Form Field ◽  
Symmetry Transformations ◽  
Augmented Superfield Formalism

We derive the off-shell nilpotent and absolutely anticommuting Becchi–Rouet–Stora–Tyutin (BRST) and anti-BRST symmetry transformations, corresponding to the (1-form) Yang–Mills (YM) and (2-form) tensorial gauge symmetries of the four (3+1)-dimensional (4D) Freedman–Townsend (FT) model, by exploiting the augmented version of Bonora–Tonin's (BT) superfield approach to BRST formalism where the 4D flat Minkowskian theory is generalized onto the (4, 2)-dimensional supermanifold. One of the novel observations is the fact that we are theoretically compelled to go beyond the horizontality condition (HC) to invoke an additional set of gauge-invariant restrictions (GIRs) for the derivation of the full set of proper (anti-)BRST symmetries. To obtain the (anti-)BRST symmetry transformations, corresponding to the tensorial (2-form) gauge symmetries within the framework of augmented version of BT-superfield approach, we are logically forced to modify the FT-model to incorporate an auxiliary 1-form field and the kinetic term for the antisymmetric (2-form) gauge field. This is also a new observation in our present investigation. We point out some of the key differences between the modified FT-model and Lahiri-model (LM) of the dynamical non-Abelian 2-form gauge theories. We also briefly mention a few similarities.

scholarly journals Symmetries and Metamorphoses

Symmetry ◽  
2020 ◽  
Vol 12 (6) ◽  
pp. 907
Author(s):  
Giuseppe Vitiello
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Arrow Of Time ◽  
Quantum Field ◽  
Continuous Symmetry ◽  
Spontaneous Breakdown ◽  
Symmetry Properties ◽  
Fractal Patterns ◽  
Symmetry Transformations ◽  
Self Similar

In quantum field theory with spontaneous breakdown of symmetry, the invariance of the dynamics under continuous symmetry transformations manifests itself in observable ordered patterns with different symmetry properties. Such a dynamical rearrangement of symmetry describes, in well definite formal terms, metamorphosis processes. The coherence of the correlations generating order and self-similar fractal patterns plays a crucial role. The metamorphosis phenomenon is generated by the loss of infrared contributions in physical states and observables due to their localized nature. The dissipative dynamics and evolution, the arising of the arrow of time and entanglement are also discussed. The conclusions may be extended to biology and neuroscience and to some aspects of linguistics in the transition from syntax to semantics (generation of meanings).

scholarly journals Christ–Lee Model: Augmented Supervariable Approach

2018 ◽  
Vol 2018 ◽  
pp. 1-12
Author(s):  
R. Kumar ◽  
A. Shukla
Keyword(s):  
Brst Symmetry ◽  
Gauge Invariant ◽  
Lee Model ◽  
Conserved Charges ◽  
Symmetry Transformations ◽  
Complete Set

We derive the complete set of off-shell nilpotent and absolutely anticommuting (anti-)BRST as well as (anti-)co-BRST symmetry transformations for the gauge-invariant Christ–Lee model by exploiting the celebrated (dual-)horizontality conditions together with the gauge-invariant and (anti-)co-BRST invariant restrictions within the framework of geometrical “augmented” supervariable approach to BRST formalism. We show the (anti-)BRST and (anti-)co-BRST invariances of the Lagrangian in the context of supervariable approach. We also provide the geometrical origin and capture the key properties associated with the (anti-)BRST and (anti-)co-BRST symmetry transformations (and corresponding conserved charges) in terms of the supervariables and Grassmannian translational generators.

scholarly journals (Anti-)chiral supervariable approach to nilpotent and absolutely anticommuting conserved charges of reparametrization invariant theories: A couple of relativistic toy models as examples

2018 ◽  
Vol 33 (22) ◽  
pp. 1850133 ◽  
Author(s):  
S. KUMAR ◽  
B. Chauhan ◽  
R. P. Malik
Keyword(s):  
Relativistic Particle ◽  
The Novel ◽  
Conserved Charges ◽  
Free Scalar ◽  
Brst Invariance

We exploit the potential and power of the Becchi–Rouet–Stora–Tyutin (BRST) and anti-BRST invariant restrictions on the (anti-)chiral supervariables to derive the proper nilpotent (anti-)BRST symmetries for the reparametrization invariant one (0[Formula: see text]+[Formula: see text]1)-dimensional (1D) toy models of a free relativistic particle as well as a free spinning (i.e. supersymmetric) relativistic particle within the framework of (anti-)chiral supervariable approach to BRST formalism. Despite the (anti-)chiral super expansions of the (anti-)chiral supervariables, we observe that the (anti-)BRST charges, for the above toy models, turn out to be absolutely anticommuting in nature. This is one of the novel observations of our present endeavor. For this proof, we utilize the beauty and strength of Curci–Ferrari (CF)-type restriction in the context of a spinning relativistic particle but no such restriction is required in the case of a free scalar relativistic particle. We have also captured the nilpotency property of the conserved charges as well as the (anti-)BRST invariance of the appropriate Lagrangian(s) of our present toy models within the framework of (anti-)chiral supervariable approach.

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