Hamilton-Jakobi method for classical mechanics in Grassmann algebra
نویسنده
چکیده
The problem of Lagrangian and Hamiltonian mechanics with Grassmann variables has been discussed previously in works [1, 2, 3] and an examples of solutions for classical systems were presented. In this paper we propose the Hamilton-Jakobi method for the solution of the classical counterpart of Witten‘s model [4]. We assume that the states of mechanical system are described by the set of ordinary bosonic degrees of freedom q (even Grassmann numbers) and the set of fermionic degrees of freedom ψ (odd Grassmann numbers). The Hamilton-Jakobi equation in the case of the classical mechanics with constrains in Grassmann algebra is following:
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