Degenerate odd poisson bracket on grassmann variables

A Poisson Bracket on Multisymplectic Phase Space ∗

A new Poisson bracket for Hamiltonian forms on the full multisymplectic phase space is defined. At least for forms of degree n − 1, where n is the dimension of space-time, Jacobi's identity is fulfilled.

Supersymmetry without Grassmann variables

Supersymmetry transformations may be represented by unitary operators in a formulation of supersymmetry without numbers that anti-commute. The physical relevance of this formulation hinges on whether or not one may add states of even and odd fermion number, a question which soon may be settled by experiment.

Supersymmetry without Grassmann variables

0 M ar 1 99 5 Odd Poisson Bracket in Hamilton ’ s Dynamics

Some applications of the odd Poisson bracket to the description of the classical and quantum dynamics are represented.

Vol. Xx (xxxx) a Poisson Bracket on Multisymplectic Phase Space *

A new Poisson bracket for Hamiltonian forms on the full multisymplectic phase space is defined. At least for forms of degree n − 1, where n is the dimension of space-time, Jacobi's identity is fulfilled.