منابع مشابه
Evaluating Grassmann Integrals
I discuss a simple numerical algorithm for the direct evaluation of multiple Grassmann integrals. The approach is exact, suffers no Fermion sign problems, and allows arbitrarily complicated interactions. Memory requirements grow exponentially with the interaction range and the transverse size of the system. Low dimensional systems of order a thousand Grassmann variables can be evaluated on a wo...
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In quantum field theory fermions are usually treated via integrals over anti-commuting Grassmann variables [2], providing an elegant framework for the formal establishment of Feynman perturbation theory. With non-perturbative approaches, such as Monte Carlo studies on the lattice, these objects are more problematic. Essentially all approaches formally integrate the fermionic fields in terms of ...
متن کاملPath Integrals with Generalized Grassmann Variables
We construct path integral representations for the evolution operator of q-oscillators with root of unity values of q-parameter using BargmannFock representations with commuting and non-commuting variables, the differential calculi being q-deformed in both cases. For q = −1 we obtain a new form of Grassmann-like path integral. on leave of absence from Nuclear Physics Institute, Moscow State Uni...
متن کاملEvaluating Integrals Using Self-Similarity
There are more advanced methods, especially Cauchy's residue calculus using complex variable theory, but a typical calculus course mentions only these two methods. Students quickly learn from experience that Archimedes really was a genius, but for practical purposes the Fundamental Theorem is the way to go. But there is a third method, which is quite elementary although not well known. It is de...
متن کاملEvaluating Some Integrals with Maple
This paper uses the mathematical software Maple for the auxiliary tool to evaluate two types of integrals. We can obtain the closed forms of these two types of integrals by using Euler's formula, DeMoivre's formula, and finite geometric series. In addition, we provide two integrals to do calculation practically. The research methods adopted in this study involved finding solutions through manua...
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ژورنال
عنوان ژورنال: Physical Review Letters
سال: 1998
ISSN: 0031-9007,1079-7114
DOI: 10.1103/physrevlett.81.3555