ORDERING, SYMBOLS AND FINITE-DIMENSIONAL APPROXIMATIONS OF PATH-INTEGRALS

We derive general form of finite-dimensional approximations of path in tegrals for both bosonic and fermionic canonical systems in terms of s ymbols of operators determined by operator ordering. We argue that for a system with a given quantum Hamiltonian such approximations are ind ependent of the type of symbols up to terms of O(epsilon), where epsil on is infinitesimal time interval determining the accuracy of the appr oximations. A new class of such approximations is found for both c-num ber and Grassmannian dynamical variables. The actions determined by th e approximations are non-local and have no classical continuum limit e xcept the cases of pq- and qp-ordering. As an explicit example the fer mionic oscillator is considered in detail.