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Advances in Mathematical Physics
Volume 2017 (2017), Article ID 9343717, 9 pages
Research Article

On Quantum Statistical Mechanics: A Study Guide

1Institute of Theoretical Physics and Astrophysics, The University of Gdansk, Wita Stwosza 57, Gdansk 80-952, Poland
2Unit for BMI, North-West University, Potchefstroom, South Africa

Correspondence should be addressed to Wladyslaw Adam Majewski;

Received 26 April 2017; Revised 2 August 2017; Accepted 9 August 2017; Published 23 November 2017

Academic Editor: Remi Léandre

Copyright © 2017 Wladyslaw Adam Majewski. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We provide an introduction to a study of applications of noncommutative calculus to quantum statistical physics. Centered on noncommutative calculus, we describe the physical concepts and mathematical structures appearing in the analysis of large quantum systems and their consequences. These include the emergence of algebraic approach and the necessity of employment of infinite-dimensional structures. As an illustration, a quantization of stochastic processes, new formalism for statistical mechanics, quantum field theory, and quantum correlations are discussed.