In the framework of superfield formalism, we discuss some aspects of the cohomological features of a two (1 + 1)-dimensional free Abelian gauge theory described by a Becchi-Rouet-Stora-Tyutin (BRST) invariant Lagrangian density. We demonstrate that the conserved and nilpotent (anti-)BRSTand (anti-)co-BRST charges are the generators of translations along the Grassmannian directions of the four (...

A condensed introduction to quantum gauge theories is given in the perturbative S-matrix framework; path integral methods are used nowhere. This approach emphasizes the fact that it is not necessary to start from classical gauge theories which are then subject to quantization, but it is also possible to recover the classical group structure and coupling properties from purely quantum mechanical...

We deduce the canonical brackets for a two (1 + 1)-dimensional (2D) free Abelian 1-form gauge theory by exploiting the beauty and strength of the continuous symmetries of a Becchi-Rouet-Stora-Tyutin (BRST) invariant Lagrangian density that respects, in totality, six continuous symmetries. All these symmetries lead to the derivation of exactly the same canonical brackets amongst the creation and...

Covariant quantization of the Nambu-Goto spinning particle in 2+1-dimensions is studied. The model is relevant in the context of recent activities in non-commutative space-time. From a technical point of view also covariant quantization of the model poses an interesting problem: the set of second class constraints (in the Dirac classification scheme) is reducible. The reducibility problem is an...

Two-dimensional quantum gravity is identified as a second-class system which we convert into a first-class system via the Batalin-Fradkin (BF) procedure. Using the extended phase space method, we then formulate the theory in most general class of gauges. The conformal gauge action suggested by David, Distler and Kawai is derived from a first principle. We find a local, light-cone gauge action w...

The local, covariant, continuous, anticommuting and nilpotent Becchi-RouetStora-Tyutin (BRST) and anti-BRST symmetry transformations for all the fields of a (0 + 1)-dimensional spinning relativistic particle are obtained in the framework of augmented superfield approach to BRST formalism. The trajectory of this super-particle, parametrized by a monotonically increasing evolution parameter τ , i...

We show the existence of a time-space noncommutativity (NC) for the physical system of a massive relativistic particle by exploiting the underlying symmetry properties of this system. The space-space NC is eliminated by the consideration of the exact symmetry properties and their consistency with the equations of motion for the above system. The symmetry corresponding to the noncommutative geom...

We show the existence of a time-space noncommutativity (NC) for the physical system of a massive relativistic particle by exploiting the underlying symmetry properties of this system. The space-space NC is eliminated by the consideration of the exact symmetry properties and their consistency with the equations of motion for the above system. The symmetry corresponding to the noncommutative geom...

We discuss the (dual-)gauge transformations for the gauge-fixed Lagrangian density and establish their intimate connection with the translation subgroup T (2) of the Wigner’s little group for the free one-form Abelian gauge theory in four (3+1)-dimensions (4D) of spacetime. Though the relationship between the usual gauge transformation for the Abelian massless gauge field and T (2) subgroup of ...

We revisit two classic Thouless–Anderson–Palmer (TAP) studies of the Sherrington–Kirkpatrick model (Bray A J and Moore M A 1980 J. Phys. C: Solid State Phys. 13 L469; De Dominicis C and Young A P 1983 J. Phys. A: Math. Gen. 16 2063). By using the Becchi–Rouet–Stora–Tyutin (BRST) supersymmetry, we prove the general equivalence of TAP and replica partition functions, and show that the annealed ca...