The calculus of local variational differential operators introduced by B. L. Voronov, I. V. Tyutin, and Sh. S. Shakhverdiev is studied in the context of jet super space geometry. In a coordinate-free way, we relate these operators to variational multivectors, for which we introduce and compute the variational Poisson and Schouten brackets by means of a unifying algebraic scheme. We give a geome...

A consistent framework has been put forward to quantize the isentropic, compressible and inviscid fluid model in the Hamiltonian framework, using the Clebsch parameterization. The naive quantization is hampered by the non-canonical (in particular field dependent) Poisson Bracket algebra. To overcome this problem, the Batalin-Tyutin [11] quantization formalism is adopted in which the original sy...

In the framework of superfield approach to Becchi-Rouet-Stora-Tyutin (BRST) formalism, the derivation of the (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 D...

We show that the Grassmannian independence of the super Lagrangian density, expressed in terms of the superfields defined on a (4, 2)-dimensional supermanifold, is a clear-cut proof for the Becchi-Rouet-Stora-Tyutin (BRST) and anti-BRST invariance of the corresoponding four (3 + 1)-dimensional (4D) Lagrangian density that describes the interaction between the U(1) gauge field and the charged co...

We discuss various symmetry properties of the reparametrization invariant toy model of a free non-relativistic particle and show that its commutativity and noncommutativity (NC) properties are the artifact of the underlying symmetry transformations. For the case of the symmetry transformations corresponding to the noncommutative geometry, the mass parameter of the toy model turns out to be nonc...

D.M. Gitman, A.D. Levin, I.V. Tyutin, and B.L. Voronov Institute of Physics, University of Sao Paulo, Brazil Lebedev Physical Institute, Moscow, Russia The electronic struture of an atom with Z ≤ Zc = 137 can be described by the Dirac equation with the Coulomb field of a point charge Ze. It was believed that the Dirac equation with Z > Zc is inconsistent and physically meaningless because the f...

In the framework of usual superfield approach, we derive the exact local, covari-ant, continuous and off-shell nilpotent Becchi-Rouet-Stora-Tyutin (BRST) and anti-BRST symmetry transformations for the U(1) gauge field (A µ) and the (anti-)ghost fields ((¯ C)C) of the Lagrangian density of a four (3 + 1)-dimensional QED by exploiting the horizontality condition defined on the six (4 + 2)-dimensi...

We demonstrate that the known off-shell nilpotent (i.e. s(a)b = 0) and anticommuting (i.e. sbsab + sabsb = 0) Becchi-Rouet-Stora-Tyutin (BRST) transformations (sb) and anti-BRST transformations (sab) are the symmetry transformations of the appropriate Lagrangian densities of a four (3 + 1)-dimensional (4D) free Abelian 2-form gauge theory which do not explicitly incorporate a very specific cons...

In the framework of usual superfield approach, we derive the exact local, covari-ant, continuous and off-shell nilpotent Becchi-Rouet-Stora-Tyutin (BRST) and anti-BRST symmetry transformations for the U(1) gauge field (A µ) and the (anti-)ghost fields ((¯ C)C) of the Lagrangian density of a four (3 + 1)-dimensional QED by exploiting the horizontality condition defined on the six (4, 2)-dimensio...

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...