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 Universal Superspace Unitary Operator and Nilpotent (Anti-)Dual-BRST Symmetries: Superfield Formalism

2016 ◽  
Vol 2016 ◽  
pp. 1-17
Author(s):  
T. Bhanja ◽  
N. Srinivas ◽  
R. P. Malik
Keyword(s):  
Gauge Theories ◽  
Unitary Operator ◽  
Group Structure ◽  
Brst Symmetry ◽  
Rigid Rotor ◽  
Unitary Operators ◽  
Bosonic Field ◽  
Hermitian Conjugate ◽  
Symmetry Transformations ◽  
The One

We exploit the key concepts of the augmented version of superfield approach to Becchi-Rouet-Stora-Tyutin (BRST) formalism to derive the superspace (SUSP)dualunitary operator and its Hermitian conjugate and demonstrate their utility in the derivation of the nilpotent and absolutely anticommuting (anti-)dual-BRST symmetry transformations for a set of interesting models of theAbelian1-form gauge theories. These models are the one (0+1)-dimensional (1D) rigid rotor and modified versions of the two (1+1)-dimensional (2D) Proca as well as anomalous gauge theories and 2D model of a self-dual bosonic field theory. We show theuniversalityof the SUSPdualunitary operator and its Hermitian conjugate in the cases ofallthe Abelian models under consideration. These SUSP dual unitary operators, besides maintaining the explicit group structure, provide the alternatives to the dual horizontality condition (DHC) and dual gauge invariant restrictions (DGIRs) of the superfield formalism. The derivations of thedualunitary operators and corresponding (anti-)dual-BRST symmetries are completelynovelresults in our present investigation.

scholarly journals (Anti-)chiral superfield approach to interacting Abelian 1-form gauge theories: Nilpotent and absolutely anticommuting charges

2018 ◽  
Vol 33 (04) ◽  
pp. 1850026 ◽  
Author(s):  
B. Chauhan ◽  
S. Kumar ◽  
R. P. Malik
Keyword(s):  
Gauge Theories ◽  
Brst Symmetry ◽  
Scalar Fields ◽  
The Novel ◽  
Complex Scalar ◽  
Symmetry Transformations ◽  
Brst Invariance ◽  
Lagrangian Densities ◽  
Chiral Superfield ◽  
Chiral Superfields

We derive the off-shell nilpotent (fermionic) (anti-)BRST symmetry transformations by exploiting the (anti-)chiral superfield approach (ACSA) to Becchi–Rouet–Stora–Tyutin (BRST) formalism for the interacting Abelian 1-form gauge theories where there is a coupling between the U(1) Abelian 1-form gauge field and Dirac as well as complex scalar fields. We exploit the (anti-)BRST invariant restrictions on the (anti-)chiral superfields to derive the fermionic symmetries of our present D-dimensional Abelian 1-form gauge theories. The novel observation of our present investigation is the derivation of the absolute anticommutativity of the nilpotent (anti-)BRST charges despite the fact that our ordinary D-dimensional theories are generalized onto the (D,[Formula: see text]1)-dimensional (anti-) chiral super-submanifolds (of the general (D,[Formula: see text]2)-dimensional supermanifold) where only the (anti-)chiral super expansions of the (anti-)chiral superfields have been taken into account. We also discuss the nilpotency of the (anti-)BRST charges and (anti-)BRST invariance of the Lagrangian densities of our present theories within the framework of ACSA to BRST formalism.

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 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 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 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 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.

scholarly journals AUGMENTED SUPERFIELD APPROACH TO NON-YANG–MILLS SYMMETRIES OF JACKIW–PI MODEL: NOVEL OBSERVATIONS

2013 ◽  
Vol 28 (06) ◽  
pp. 1350011 ◽  
Author(s):  
SAURABH GUPTA ◽  
R. KUMAR
Keyword(s):  
Gauge Theories ◽  
Brst Symmetry ◽  
Auxiliary Field ◽  
The Novel ◽  
Yang Mills ◽  
Symmetry Transformations ◽  
Augmented Superfield Formalism

We derive the off-shell nilpotent and absolutely anti-commuting Becchi–Rouet–Stora–Tyutin (BRST) as well as anti-BRST symmetry transformations corresponding to the non-Yang–Mills (NYM) symmetry transformations of (2+1)-dimensional Jackiw–Pi (JP) model within the framework of "augmented" superfield formalism. The Curci–Ferrari (CF) restriction, which is a hallmark of non-Abelian one-form gauge theories, does not appear in this case. One of the novel features of our present investigation is the derivation of proper (anti-)BRST symmetry transformations corresponding to the auxiliary field ρ that cannot be derived by any conventional means.

scholarly journals Nilpotent charges in an interacting gauge theory and an 𝒩 = 2 SUSY quantum mechanical model: (Anti-)chiral superfield approach

2019 ◽  
Vol 34 (24) ◽  
pp. 1950131 ◽  
Author(s):  
B. Chauhan ◽  
S. Kumar ◽  
R. P. Malik
Keyword(s):  
Gauge Theory ◽  
Harmonic Oscillator ◽  
Gauge Field ◽  
Mechanical Model ◽  
Brst Symmetry ◽  
Quantum Mechanical ◽  
Gauge Invariant ◽  
Symmetry Transformations ◽  
Invariant Coupling ◽  
Chiral Superfield

We exploit the power and potential of the (anti-)chiral superfield approach (ACSA) to Becchi–Rouet–Stora–Tyutin (BRST) formalism to derive the nilpotent (anti-)BRST symmetry transformations for any arbitrary [Formula: see text]-dimensional interacting non-Abelian 1-form gauge theory where there is an [Formula: see text] gauge invariant coupling between the gauge field and the Dirac fields. We derive the conserved and nilpotent (anti-)BRST charges and establish their nilpotency and absolute anticommutativity properties within the framework of ACSA to BRST formalism. The clinching proof of the absolute anticommutativity property of the conserved and nilpotent (anti-)BRST charges is a novel result in view of the fact that we consider, in our endeavor, only the (anti-)chiral super expansions of the superfields that are defined on the [Formula: see text]-dimensional super-submanifolds of the general [Formula: see text]-dimensional supermanifold on which our [Formula: see text]-dimensional ordinary interacting non-Abelian 1-form gauge theory is generalized. To corroborate the novelty of the above result, we apply the ACSA to an [Formula: see text] supersymmetric (SUSY) quantum mechanical (QM) model of a harmonic oscillator and show that the nilpotent and conserved [Formula: see text] supercharges of this system do not absolutely anticommute.

scholarly journals Supervariable Approach to the Nilpotent Symmetries for a Toy Model of the Hodge Theory

2016 ◽  
Vol 2016 ◽  
pp. 1-13 ◽  
Author(s):  
D. Shukla ◽  
T. Bhanja ◽  
R. P. Malik
Keyword(s):  
Brst Symmetry ◽  
Hodge Theory ◽  
Present Theory ◽  
Rigid Rotor ◽  
Geometrical Meaning ◽  
Horizontality Condition ◽  
Symmetry Transformations ◽  
Brst Invariance ◽  
Standard Techniques

We exploit the standard techniques of the supervariable approach to derive the nilpotent Becchi-Rouet-Stora-Tyutin (BRST) and anti-BRST symmetry transformations for a toy model of the Hodge theory (i.e., a rigid rotor) and provide the geometrical meaning and interpretation to them. Furthermore, wealsoderive the nilpotent (anti-)co-BRST symmetry transformations for this theory within the framework of the above supervariable approach. We capture the (anti-)BRST and (anti-)co-BRST invariance of the Lagrangian of our present theory within the framework of augmented supervariable formalism. We also express the (anti-)BRST and (anti-)co-BRST charges in terms of the supervariables (obtained after the application of the (dual-)horizontality conditions and (anti-)BRST and (anti-)co-BRST invariant restrictions) to provide the geometrical interpretations for their nilpotency and anticommutativity properties. The application of the dual-horizontality condition and ensuing proper (i.e., nilpotent and absolutely anticommuting) fermionic (anti-)co-BRST symmetries are completelynovelresults in our present investigation.

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