scholarly journals Christ–Lee Model: (Anti-)chiral Supervariable Approach to BRST Formalism

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
B. Chauhan ◽  
S. Kumar
Keyword(s):  
Crucial Role ◽  
Brst Symmetry ◽  
Lee Model ◽  
Conserved Charges ◽  
Quantum Symmetry ◽  
Symmetry Transformations

We derive the off-shell nilpotent of order two and absolutely anticommuting Becchi-Rouet-Stora-Tyutin (BRST), anti-BRST, and (anti-)co-BRST symmetry transformations for the Christ–Lee (CL) model in one 0 + 1 -dimension (1D) of spacetime by exploiting the (anti-)chiral supervariable approach (ACSA) to BRST formalism where the quantum symmetry (i.e., (anti-)BRST along with (anti-)co-BRST) invariant quantities play a crucial role. We prove the nilpotency and absolute anticommutativity properties of the (anti-)BRST along with (anti-)co-BRST conserved charges within the scope of ACSA to BRST formalism where we take only one Grassmannian variable into account. We also show the (anti-)BRST and (anti-)co-BRST invariances of the Lagrangian within the scope of ACSA.

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 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 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 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 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 Superfield Approach to Nilpotency and Absolute Anticommutativity of Conserved Charges: 2D Non-Abelian 1-Form Gauge Theory

2018 ◽  
Vol 2018 ◽  
pp. 1-23 ◽  
Author(s):  
S. Kumar ◽  
B. Chauhan ◽  
R. P. Malik
Keyword(s):  
Gauge Theory ◽  
Brst Symmetry ◽  
Theoretical Strength ◽  
Conserved Charges ◽  
Lagrangian Densities ◽  
Matter Fields ◽  
Chiral Superfields

We exploit the theoretical strength of augmented version of superfield approach (AVSA) to Becchi-Rouet-Stora-Tyutin (BRST) formalism to express the nilpotency and absolute anticommutativity properties of the (anti-)BRST and (anti-)co-BRST conserved charges for the two (1+1)-dimensional (2D) non-Abelian 1-form gauge theory (without any interaction with matter fields) in the language of superspace variables, their derivatives, and suitable superfields. In the proof of absolute anticommutativity property, we invoke the strength of Curci-Ferrari (CF) condition for the (anti-)BRST charges. No such outside condition/restriction is required in the proof of absolute anticommutativity of the (anti-)co-BRST conserved charges. The latter observation (as well as other observations) connected with (anti-)co-BRST symmetries and corresponding conserved charges are novel results of our present investigation. We also discuss the (anti-)BRST and (anti-)co-BRST symmetry invariance of the appropriate Lagrangian densities within the framework of AVSA. In addition, we dwell a bit on the derivation of the above fermionic (nilpotent) symmetries by applying the AVSA to BRST formalism, where only the (anti)chiral superfields are used.

scholarly journals On augmented superfield approach to vector Schwinger model

2016 ◽  
Vol 31 (34) ◽  
pp. 1650173 ◽  
Author(s):  
Saurabh Gupta ◽  
R. Kumar
Keyword(s):  
Brst Symmetry ◽  
Geometrical Interpretation ◽  
Schwinger Model ◽  
Symmetry Transformations ◽  
Augmented Superfield Formalism

We exploit the techniques of Bonora–Tonin superfield formalism to derive the off-shell nilpotent and absolutely anticommuting (anti-)BRST as well as (anti-)co-BRST symmetry transformations for the (1[Formula: see text]+[Formula: see text]1)-dimensional (2D) bosonized vector Schwinger model. In the derivation of above symmetries, we invoke the (dual)-horizontality conditions as well as gauge and (anti-)co-BRST invariant restrictions on the superfields that are defined onto the (2,[Formula: see text]2)-dimensional supermanifold. We provide geometrical interpretation of the above nilpotent symmetries (and their corresponding charges). We also express the nilpotency and absolute anticommutativity of the (anti-)BRST and (anti-)co-BRST charges within the framework of augmented superfield formalism.

scholarly journals Augmented Superfield Approach to Nilpotent Symmetries of the Modified Version of 2D Proca Theory

2015 ◽  
Vol 2015 ◽  
pp. 1-21 ◽  
Author(s):  
A. Shukla ◽  
S. Krishna ◽  
R. P. Malik
Keyword(s):  
Differential Geometry ◽  
Lagrangian Density ◽  
Brst Symmetry ◽  
Physical Realization ◽  
Gauge Invariant ◽  
De Rham ◽  
Symmetry Transformations ◽  
Complete Set ◽  
Brst Invariance ◽  
Augmented Superfield Formalism

We derive the complete set of off-shell nilpotent and absolutely anticommuting Becchi-Rouet-Stora-Tyutin (BRST), anti-BRST, and (anti-)co-BRST symmetry transformations forallthe fields of the modified version of two(1+1)-dimensional (2D) Proca theory by exploiting the “augmented” superfield formalism where the (dual-)horizontality conditions and (dual-)gauge invariant restrictions are exploitedtogether. We capture the (anti-)BRST and (anti-)co-BRST invariance of the Lagrangian density in the language of superfield approach. We also express the nilpotency and absolute anticommutativity of the (anti-)BRST and (anti-)co-BRST charges within the framework of augmented superfield formalism. This exercise leads to somenovelobservations which have, hitherto, not been pointed out in the literature within the framework of superfield approach to BRST formalism. For the sake of completeness, we also mention, very briefly, a unique bosonic symmetry, the ghost-scale symmetry, and discrete symmetries of the theory and show that the algebra of conserved charges provides a physical realization of the Hodge algebra (satisfied by the de Rham cohomological operators of differential geometry).

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 NONCOMMUTATIVE GAUGE THEORIES: MODEL FOR HODGE THEORY

2013 ◽  
Vol 28 (25) ◽  
pp. 1350122 ◽  
Author(s):  
SUDHAKER UPADHYAY ◽  
BHABANI PRASAD MANDAL
Keyword(s):  
Differential Geometry ◽  
Compact Manifold ◽  
Gauge Theories ◽  
Brst Symmetry ◽  
Decomposition Theorem ◽  
Hodge Theory ◽  
De Rham ◽  
Symmetry Transformations ◽  
Moyal Plane ◽  
Noncommutative Gauge Theories

The nilpotent Becchi–Rouet–Stora–Tyutin (BRST), anti-BRST, dual-BRST and anti-dual-BRST symmetry transformations are constructed in the context of noncommutative (NC) 1-form as well as 2-form gauge theories. The corresponding Noether's charges for these symmetries on the Moyal plane are shown to satisfy the same algebra, as by the de Rham cohomological operators of differential geometry. The Hodge decomposition theorem on compact manifold is also studied. We show that noncommutative gauge theories are field theoretic models for Hodge theory.

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