Supersymmetry and the Odd Poisson Bracket

Details Supersymmetry and the Odd Poisson Bracket Supersymmetry and the Odd Poisson Bracket

2002-04-02

arxiv.org/abs/hep-th/0204018v1

Nucl.Phys.Proc.Suppl. 101 (2001) 26-42

Physics

High Energy Physics

High Energy Physics - Theory

17 pages, LATEX 2e. Invited talk given at the International Symposium "30 Years of Supersymmetry" (Theoretical Physics Institu

Scientific paper

10.1016/S0920-5632(01)01490-6

Some applications of the odd Poisson bracket developed by Kharkov's theorists are represented, including the reformulation of classical Hamiltonian dynamics, the description of hydrodynamics as a Hamilton system by means of the odd bracket and the dynamics formulation with the Grassmann-odd Lagrangian. Quantum representations of the odd bracket are also constructed and applied for the quantization of classical systems based on the odd bracket and for the realization of the idea of a composite spinor structure of space-time. At last, the linear odd bracket, corresponding to a semi-simple Lie group, is introduced on the Grassmann algebra.

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