Path-Integral for Quadratic Hamiltonian Systems and Boundary Conditions

Details Path-Integral for Quadratic Hamiltonian Systems and Boundary Conditions Path-Integral for Quadratic Hamiltonian Systems and Boundary Conditions

1998-10-15

arxiv.org/abs/hep-th/9810112v1

Physics

High Energy Physics

High Energy Physics - Theory

4 pages, LaTeX 2e, sprocl.sty. To be published in the Proceedings of 6-th International Conference on "Path-Integrals from peV

Scientific paper

A path-integral representation for the kernel of the evolution operator of general Hamiltonian systems is reviewed. We study the models with bosonic and fermionic degrees of freedom. A general scheme for introducing boundary conditions in the path-integral is given. We calculate the path-integral for the systems with quadratic first class constraints and present an explicit formula for the heat kernel in this case. These results may be applied to many quantum systems which can be reduced to the Hamiltonian systems with quadratic constraints (confined quarks, Calogero type models, string and $p$-brain theories, etc.).

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