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This extensive reference text summarizes the concepts and mathematical methods that are required to provide a firm foundation for advanced studies in quantum thermal physics, which underlies all current mesoscopic sciences.

The book introduces the mathematical language and fundamental physical concepts on which the entire subject of quantum statistical mechanics has been developed. Starting from the essential mathematical concepts, definitions, theorems, and formulas for the understanding and application of quantum statistical mechanics and physical sciences in general, the author provides pedagogical annotations to introduce new insights not to be found in traditional mathematics handbooks.

Each chapter is completed with a set of further reading references which contain more complete treatment of the subjects described. This comprehensive volume will serve as a text throughout advanced studies in quantum statistical physics and beyond, and as a reference for researchers in all fields of physics.

Quantum Statistical Thermodynamics: A Glossary of Mathematical and Physical Concepts

Preface.

1 Notations and Constants.

2 Elementary Algebra.

3 Elementary Calculus.

4 Combinatorics.

5 Theory of Probability.

6 Quantum Statistics.

7 Tensor Analysis.

8 Complex-Valued Functions.

9 Function Analysis.

10 Special Function.

11 Eigenvalue Problems.

12 Lenear Vector Spaces.

13 Operators in a Linear Vector Space.

14 Representations of a linear Vector.

15 Physical Spaces.

16 Operators Dirac Space.

17 Identities and Commutators of Operators.

18 Clebsh-Gordan Coefficient.

19 Wigner 3-j Symbols.

20 The 3n-j Symbols.

21 The 3-kn Symbols.

22 The Square Symbols.