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arXiv · hep-th/9401063

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

T. Kashiwa·S. Sakoda·S. V. Zenkin
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Abstract

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 $O(ε)$, where $ε$ 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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T. Kashiwa, S. Sakoda, S. V. Zenkin. 1994-01-14. Ordering, symbols, and finite-dimensional approximations of path integrals. https://doi.org/10.1143/ptp.92.669

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