arXiv subjects
Publications and source records attributed to A. P. Nersessian.
The transparent way for the invariant (Hamiltonian) description of equivariant localization of the integrals over phase space is proposed. It uses the odd symplectic structure, constructed over tangent bundle of the phase space and permits straightforward generalization for the path integrals. Simultaneously the method of supersymmetrization for a wide class of the Hamiltonian systems is derived.
An invariant definition of the operator $Δ$ of the Batalin-Vilkovisky formalism is proposed. It is defined as the divergence of a Hamiltonian vector field with an odd Poisson bracket (antibracket). Its main properties, which follow from this definition, as well as an example of realization on Kählerian supermanifolds, are considered. The geometrical meaning of the Batalin-Vilkovisky formalism is discussed.
Supergeneralization of $\DC P(N)$ provided by even and odd Kählerian structures from Hamiltonian reduction are construct.Operator $ Δ$ which used in Batalin-- Vilkovisky quantization formalism and mechanics which are bi-Hamiltonian under corresponding even and odd Poisson brackets are considered.