We present an analysis on the Becchi-Rouet-Stora-Tyutin (BRST) symmetry transformations of Ho\ifmmode \check{r}\else \v{r}\fi{}ava theory under Batalin-Fradkin-Vilkovisky quantization, both in nonprojectable and projectable cases. obtain that BRST are intimately related to a particular spatial diffeomorphism along one ghost vector fields. show explicitly invariance quantum action nilpotence tra...

We obtain an interesting realization of the de Rham cohomological operators of differential geometry in terms of the noncommutative q-superoscillators for the supersymmetric quantum group GLqp(1|1). In particular, we show that a unique quantum superalgebra, obeyed by the bilinears of fermionic and bosonic noncommutative q-(super)oscillators of GLqp(1|1), is exactly identical to that obeyed by t...

We demonstrate that the nilpotent Becchi-Rouet-Stora-Tyutin (BRST) and anti-BRST symmetry invariance of the Lagrangian density of a four (3 + 1)-dimensional (4D) non-Abelian 1-form gauge theory with Dirac fields can be captured within the framework of the superfield approach to BRST formalism. The above 4D theory, where there is an explicit coupling between the non-Abelian 1-form gauge field an...

We work out the description of gauge symmetry unimodular gravity in constrained Hamiltonian formalism. In particular, we demonstrate how transversality conditions restricting diffeomorphism parameters emerge from algebra constraints. The alternative form is long known as parametrizing volume preserving diffeomorphisms by unrestricted two-forms instead transverse vector fields. This reducible. t...

A Lagrangian formulation of the BRST quantization of generic gauge theories in general irreducible non-Abelian hypergauges is proposed on the basis of the multilevel Batalin–Tyutin formalism and a special BV–BFV dual description of a reducible gauge model on the symplectic supermanifold M0 locally parameterized by the antifields for Lagrangian multipliers and the fields of the BV method. The qu...

We exploit the geometrical superfield formalism to derive the local, covariant and continuous Becchi-Rouet-Stora-Tyutin (BRST) symmetry transformations and the non-local, non-covariant and continuous dual-BRST symmetry transformations for the free Abelian one-form gauge theory in four (3+1)-dimensions (4D) of spacetime. Our discussion is carried out in the framework of BRST invariant Lagrangian...

We provide an alternative to the gauge covariant horizontality condition which is responsible for the derivation of the nilpotent (anti-)BRST symmetry transformations for the gauge and (anti-)ghost fields of a (3 + 1)dimensional (4D) interacting 1-form non-Abelian gauge theory in the framework of the usual superfield approach to Becchi-Rouet-Stora-Tyutin (BRST) formalism. The above covariant ho...

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...