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Prog. Theor. Phys. Vol. 92 No. 3 (1994) pp. 669-685
Ordering, Symbols and Finite-Dimensional Approximations of Path Integrals
Taro Kashiwa,
Seiji Sakoda and
Sergei V. Zenkin
Department of Physics, Kyushu University, Fukuoka 812
(Received June 2, 1994)
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-ordering. As an explicit example the fermionic oscillator is considered in detail.
URL :
http://ptp.ipap.jp/link?PTP/92/669/
DOI : 10.1143/PTP.92.669
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