arXiv subjects
Publications and source records attributed to V. A. Soroka.
A principle possibility for the existence of a multiplet including the components with the different masses is indicated. This paper is dedicated to the memory of Anna Yakovlevna Gelyukh (Kalaida).
It is shown that two definitions for the exterior differential in superspace, giving the same exterior calculus, when applied to the Poisson bracket lead to the different results. Examples of the even and odd linear brackets, corresponding to semi-simple Lie groups, are given and their natural connection with BRST and anti-BRST charges is indicated.
A supersymmetric $D = 1, N =1$ model with a Grassmann-odd Lagrangian is proposed which, in contrast to the model with an even Lagrangian, contains not only a kinetic term but also an interaction term for the coordinates entering into one real scalar Grassmann-even (bosonic) superfield.
A linear odd Poisson bracket (antibracket) realized solely in terms of Grassmann variables is suggested. It is revealed that the bracket, which corresponds to a semi-simple Lie group, has at once three Grassmann-odd nilpotent $Δ$-like differential operators of the first, the second and the third orders with respect to Grassmann derivatives, in contrast with the canonical odd Poisson bracket having the only Grassmann-odd nilpotent differential $Δ$-operator of the second order. It is shown that these $Δ$-like operators together with a Grassmann-odd nilpotent Casimir function of this bracket form a finite-dimensional Lie superalgebra.
A linear degenerate odd Poisson bracket (antibracket) realized solely on Grassmann variables is presented. It is revealed that this bracket has at once three nilpotent $Δ$-like differential operators of the first, the second and the third orders with respect to the Grassmann derivatives. It is shown that these $Δ$-like operators together with the Grassmann-odd nilpotent Casimir function of this bracket form a finite-dimensional Lie superalgebra.
The action with the Grassmann-odd Lagrangian for the supersymmetric classical Witten mechanics is constructed. It is shown that the exterior differential can be used for the connection between Grassmann-even and Grassmann-odd formulations of the classical dynamics in the superspace in both Hamilton's and Lagrange's approaches.
Some applications of the odd Poisson bracket to the description of the classical and quantum dynamics are represented.