NON-PERTURBATIVE CLUSTER CUMULANT FORMALISMS FOR FINITE-TEMPERATURE SYSTEMS

Debashis Mukherjee
Department of Physical Chemistry,
Indian Association for the Cultivation of Science,
Calcutta, India


The Coupled Cluster Expansion of the many-body wave-operator has been eminently successful for trating correlation effects to high accuracy for both fermionic and bosonic systems.This has prompted attempts in recent years to extend this approach to encompass time- and temperature-dependent situations.The latter in particular may be viewed as the imaginary-time version of a real-time formulation. We shall discuss one such finite-temperature cluster-cumulant formalism which seems to share the best features of a zero-temperature coupled-cluster theory. The key theoretical ingredients of the method are (a) the notion of thermal normal ordering and Wick-like expansion theorem to simplify the imaginary-time ordered exponential representation of the Boltzmann operator, and (b) a nonperturbative normal-ordered exponential representation of the Boltzmann operator using the novel normal ordering mentioned above. The grand partition function is generated systematically as a thermal trace of the Boltzmann operator. Generalization of the concept of the normal ordering to cover imaginary-time path-integral based methods offers a nonperturbative access to systematic extensions of the usual Feynman-Kleinert and static path approximations. Brief presentations will also be made of the recent attempts to formulate cluster expansion formulations of the canonical partition function.