Formulae for Configuration Averages of Products of One-Body and Two-Body Operators in Many-Fermion Spaces

摘要

The trace reduction theorems (TRT) of J.N. Ginocchio and S. Ayik have greatly simplified the evaluation of the average expectation value of an operator in a basis of many-fermion states. Such averages are required for moment-method calculations of the statistical properties of many-fermion systems. The present work is aimed at simplifying the practical application of the TRT. Symmetries are used to detect distinct terms which have equal contributions to the operator average, and the minimum list of formulas which need be evaluated is presented. This is done for each product of one-body and two-body operators having four or fewer factors. The resulting formulas are applicable to both scalar average and configuration average calculations. (ERA citation 09:004011)