Ordering, symbols, and finite-dimensional approximations of path integrals

Details Ordering, symbols, and finite-dimensional approximations of path integrals Ordering, symbols, and finite-dimensional approximations of path integrals

1994-01-14

arxiv.org/abs/hep-th/9401063v1

Prog.Theor.Phys. 92 (1994) 669-686

Physics

High Energy Physics

High Energy Physics - Theory

20 pages (harvmac), KYUSHU-HET-12

Scientific paper

10.1143/PTP.92.669

We derive general form of finite-dimensional approximations of path integrals for both bosonic and fermionic canonical systems in terms of symbols of operators determined by operator ordering. We argue that for a system with a given quantum Hamiltonian such approximations are independent of the type of symbols up to terms of $O(\epsilon)$, where $\epsilon$ is infinitesimal time interval determining the accuracy of the approximations. A new class of such approximations is found for both c-number and Grassmannian dynamical variables. The actions determined by the approximations are non-local and have no classical continuum limit except the cases of $pq$- and $qp$-ordeeing. As an explicit example the fermionic oscillator is considered in detail.

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