# The Statistical Mechanics of Quantum Lattice Systems: A Path Integral Approach

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*Sergio Albeverio; Yuri Kondratiev; Yuri Kozitsky; Michael Röckner*

A publication of the European Mathematical Society

Quantum statistical mechanics plays a major role in many fields
such as thermodynamics, plasma physics, solid-state
physics, and the study of stellar structure. While the theory of quantum
harmonic oscillators is relatively simple, the case of anharmonic oscillators,
a mathematical model of a localized quantum particle, is more complex and
challenging. Moreover, infinite systems of interacting quantum anharmonic
oscillators possess interesting ordering properties with respect to quantum
stabilization.

This book presents a rigorous approach to the statistical mechanics of such
systems, in particular with respect to their actions on a crystal lattice.

The text is addressed to both mathematicians and physicists,
especially those who are concerned with the rigorous mathematical background of
their results and the kind of problems that arise in quantum statistical
mechanics. The reader will find here a concise collection of facts, concepts,
and tools relevant for the application of path integrals and other methods
based on measure and integration theory to problems of quantum physics, in
particular the latest results in the mathematical theory of quantum anharmonic
crystals. The methods developed in the book are also applicable to other
problems involving infinitely many variables, for example, in biology and
economics.

A publication of the European Mathematical Society (EMS). Distributed within the Americas by the American Mathematical Society.

#### Readership

Graduate students and research mathematicians interested in quantum statistical mechanics.