Quantum-Classical Correspondence

1 Towards a Non-Galilean View of Physics.- 2 Some Basics of Stochastic Processes.- 3 Classical Physics.- 4 Quantum Physics.- 5 Classical Limit of Quantum Physics.- 6 Summary and Open Questions.- A Elements of Set Theory.- A.1 Definitions.- A.2 Algebraic Structure.- A.3 Borel Field.- A.4 Set Function and Point Function.- B Quantization of the Smoluchowski Equation.- B.1 Constant Force.- B.2 Linear Force.- B.3 General Case.- C Dynamical Quantization Versus Dirac Quantization.- D Dynamical Quantization Versus Feynman Quantization.- E Wigner Representation of Classical Mechanics.- E.1 Dynamics.- E.2 Kinematics.- References.

From the reviews:



"The present book aims to present the author's new approaches to quantization and classical limit ... . The book contains a lot of material concerning the applied methods before the author's propositions. There are enough references to cover the needs of the presentation. ... The book is interesting and easy to read." (Demetris P.K. Ghikas, Mathematical Reviews, 2005e)

"The book is devoted to the quantization problem, i.e. how to do a quantum description starting from a classical one, and to dequantization ... . the mathematician will find a nice presentation of some classical and open problems in the theory of quantization and dequantization of open systems and a lot of references to classical articles." (Stefan Berceanu, Zentralblatt MATH, Vol. 1074, 2005)

"The aim of the book is extremely ambitious. It is intended to given account of the relationship between quantum physics and classical physics. ... A quite comprehensive list of 272 references provides a very useful support for further study on the subject. The dynamical quantization proposed by the author surely is interesting in itself. ... In conclusion, the interested reader will find this book very challenging. The analysis and criticism of the proposed dynamical quantization method are a good argument of research." (Francesco Guerra, Meccanica, Vol. 42, 2007)