General theory of fractal path integrals with applications to many‐body theories and statistical physics

Suzuki, Masuo

doi:10.1063/1.529425

General theory of fractal path integrals with applications to many‐body theories and statistical physics

Masuo Suzuki

Feb 1, 1991

Published in:

J.Math.Phys. 32 (1991) 2, 400

Published: Feb 1, 1991

DOI:

10.1063/1.529425

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Abstract: (AIP)

A general scheme of fractal decomposition of exponential operators is presented in any order m. Namely, exp[x(A+B)]=Sm(x)+O(xm+1) for any positive integer m, where Sm(x)=et1A et2B et3A et4B⋅⋅⋅etMA with finite M depending on m. A general recursive scheme of construction of {tj} is given explicitly. It is proven that some of {tj} should be negative for m≥3 and for any finite M (nonexistence theorem of positive decomposition). General systematic decomposition criterions based on a new type of time‐ordering are also formulated. The decomposition exp[x(A+B)]=[Sm(x/n)]n +O(xm+1/nm) yields a new efficient approach to quantum Monte Carlo simulations.

References(20)

Figures(0)

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