Procedings of the 3nd International Conference "Mathematical Physics and its Applications"
Complex Systems, Quantum Mechanics, Information Theory

High temperature heat kernel expansion and its applications

V. V. Mikheyev

Omsk State Technical University, Omsk, 644050, Russia

Abstract: The algorithm constructed to build the high-temperature heat kernel expansion and the statistic sum on the noncompact Lie groups manifolds is discussed in the article. The method is based on the formalism of non-commutative integration which originated from the coadjoint orbits' approach to the problems of integration and quantization. Applications of presented method to the problems of quantum statistic mechanics and quantum field theory are also discussed.

Keywords: heat kernel, statistic sum, partition function, non-commutative integration, high-temperature asymptotics, effective lagrangian.

UDC: 51:530.145

MSC: Primary 22E70, 81S10; Secondary 35P99, 81Q05, 81Q99

Original article submitted 16/XI/2012
revision submitted – 27/I/2013

DOI: 10.14498/vsgtu1183

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