scholarly journals NILPOTENT SYMMETRIES FOR MATTER FIELDS IN NON-ABELIAN GAUGE THEORY: AUGMENTED SUPERFIELD FORMALISM

2005 ◽  
Vol 20 (20n21) ◽  
pp. 4899-4915 ◽  
Author(s):  
R. P. MALIK
Keyword(s):  
Gauge Theory ◽  
General Scheme ◽  
Brst Symmetry ◽  
Grassmann Algebra ◽  
Abelian Gauge ◽  
Abelian Gauge Theory ◽  
Symmetry Transformations ◽  
Matter Fields ◽  
Augmented Superfield Formalism ◽  
Standing Problem

In the framework of superfield approach to Becchi–Rouet–Stora–Tyutin (BRST) formalism, the derivation of the BRST and anti-BRST nilpotent symmetry transformations for the matter fields, present in any arbitrary interacting gauge theory, has been a long-standing problem. In our present investigation, the local, covariant, continuous and off-shell nilpotent (anti-)BRST symmetry transformations for the Dirac fields [Formula: see text] are derived in the framework of the augmented superfield formulation where the four (3 + 1)-dimensional (4D) interacting non-Abelian gauge theory is considered on the six (4 + 2)-dimensional supermanifold parametrized by the four even space–time coordinates xμ and a couple of odd elements (θ and [Formula: see text]) of the Grassmann algebra. The requirement of the invariance of the matter (super)currents and the horizontality condition on the (super)manifolds leads to the derivation of the nilpotent symmetries for the matter fields as well as the gauge and the (anti)ghost fields of the theory in the general scheme of augmented superfield formalism.

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 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 A NOVEL SYMMETRY FOR NON-ABELIAN GAUGE THEORY

2002 ◽  
Vol 17 (03) ◽  
pp. 185-196 ◽  
Author(s):  
R. P. MALIK
Keyword(s):  
Gauge Theory ◽  
Lagrangian Density ◽  
Brst Symmetry ◽  
Geometrical Interpretation ◽  
Abelian Gauge ◽  
Abelian Gauge Theory ◽  
Conserved Charges ◽  
Continuous Symmetries ◽  
Matter Fields

In the framework of superfield formalism, we demonstrate the existence of a new local, covariant, continuous and nilpotent (dual-BRST) symmetry for the BRST invariant Lagrangian density of a self-interacting two (1+1)-dimensional (2D) non-Abelian gauge theory (having no interaction with matter fields). The local and nilpotent Noether conserved charges corresponding to the above continuous symmetries find their geometrical interpretation as the translation generators along the odd (Grassmannian) directions of the four (2+2)-dimensional compact supermanifold.

scholarly journals Nilpotent symmetries and Curci–Ferrari-type restrictions in 2D non-Abelian gauge theory: Superfield approach

2017 ◽  
Vol 32 (33) ◽  
pp. 1750193 ◽  
Author(s):  
N. Srinivas ◽  
R. P. Malik
Keyword(s):  
Gauge Theory ◽  
The Self ◽  
Abelian Gauge ◽  
Abelian Gauge Theory ◽  
Abelian Theory ◽  
Matter Fields

We derive the off-shell nilpotent symmetries of the two [Formula: see text]-dimensional (2D) non-Abelian 1-form gauge theory by using the theoretical techniques of the geometrical superfield approach to Becchi–Rouet–Stora–Tyutin (BRST) formalism. For this purpose, we exploit the augmented version of superfield approach (AVSA) and derive theoretically useful nilpotent (anti-)BRST, (anti-)co-BRST symmetries and Curci–Ferrari (CF)-type restrictions for the self-interacting 2D non-Abelian 1-form gauge theory (where there is no interaction with matter fields). The derivation of the (anti-)co-BRST symmetries and all possible CF-type restrictions are completely novel results within the framework of AVSA to BRST formalism where the ordinary 2D non-Abelian theory is generalized onto an appropriately chosen [Formula: see text]-dimensional supermanifold. The latter is parametrized by the superspace coordinates [Formula: see text] where [Formula: see text] (with [Formula: see text]) are the bosonic coordinates and a pair of Grassmannian variables [Formula: see text] obey the relationships: [Formula: see text], [Formula: see text]. The topological nature of our 2D theory allows the existence of a tower of CF-type restrictions.

scholarly journals ONE-FORM ABELIAN GAUGE THEORY AS THE HODGE THEORY

2007 ◽  
Vol 22 (21) ◽  
pp. 3521-3562 ◽  
Author(s):  
R. P. MALIK
Keyword(s):  
Gauge Theory ◽  
Theoretical Model ◽  
Equations Of Motion ◽  
Hodge Theory ◽  
Laplacian Operator ◽  
Abelian Gauge ◽  
Abelian Gauge Theory ◽  
De Rham ◽  
Symmetry Transformations ◽  
Field Theoretical Model

We demonstrate that the two (1+1)-dimensional (2D) free 1-form Abelian gauge theory provides an interesting field theoretical model for the Hodge theory. The physical symmetries of the theory correspond to all the basic mathematical ingredients that are required in the definition of the de Rham cohomological operators of differential geometry. The conserved charges, corresponding to the above continuous symmetry transformations, constitute an algebra that is reminiscent of the algebra obeyed by the de Rham cohomological operators. The topological features of the above theory are discussed in terms of the BRST and co-BRST operators. The super-de Rham cohomological operators are exploited in the derivation of the nilpotent (anti-)BRST, (anti-)co-BRST symmetry transformations and the equations of motion for all the fields of the theory, within the framework of the superfield formulation. The derivation of the equations of motion, by exploiting the super-Laplacian operator, is a completely new result in the framework of the superfield approach to BRST formalism. In an Appendix, the interacting 2D Abelian gauge theory (where there is a coupling between the U(1) gauge field and the Dirac fields) is also shown to provide a tractable field theoretical model for the Hodge theory.

scholarly journals Some novel features in 2D non-Abelian theory: BRST approach

2017 ◽  
Vol 32 (22) ◽  
pp. 1750136 ◽  
Author(s):  
N. Srinivas ◽  
S. Kumar ◽  
B. K. Kureel ◽  
R. P. Malik
Keyword(s):  
Gauge Theory ◽  
Lagrange Multipliers ◽  
Brst Symmetry ◽  
Abelian Theory ◽  
Symmetry Transformations ◽  
Lagrangian Densities ◽  
Matter Fields

Within the framework of Becchi–Rouet–Stora–Tyutin (BRST) formalism, we discuss some novel features of a two (1[Formula: see text]+[Formula: see text]1)-dimensional (2D) non-Abelian 1-form gauge theory (without any interaction with matter fields). Besides the usual off-shell nilpotent and absolutely anticommutating (anti-)BRST symmetry transformations, we discuss the off-shell nilpotent and absolutely anticommutating (anti-)co-BRST symmetry transformations. Particularly, we lay emphasis on the existence of the coupled (but equivalent) Lagrangian densities of the 2D non-Abelian theory in view of the presence of (anti-)co-BRST symmetry transformations where we pin-point some novel features associated with the Curci–Ferrari (CF-)type restrictions. We demonstrate that these CF-type restrictions can be incorporated into the (anti-)co-BRST invariant Lagrangian densities through the fermionic Lagrange multipliers which carry specific ghost numbers. The modified versions of the Lagrangian densities (where we get rid of the new CF-type restrictions) respect some precise symmetries as well as a couple of symmetries with CF-type constraints. These observations are completely novel as far as the BRST formalism, with proper (anti-)co-BRST symmetries, is concerned.

Regge behavior of spontaneously broken non-Abelian gauge theory

1978 ◽  
Vol 17 (2) ◽  
pp. 585-597 ◽  
Author(s):  
J. B. Bronzan ◽  
R. L. Sugar
Keyword(s):  
Gauge Theory ◽  
Abelian Gauge ◽  
Abelian Gauge Theory ◽  
Regge Behavior
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