The Method of Second Quantization (Monographs and Textbooks in Pure and Applied Physics, Vol. 24)

The Method of Second Quantization deals with the method of second quantization and its use to solve problems of quantum mechanics involving an indefinite number of particles, mainly in field theory and quantum statistics. Topics covered include operations on generating functionals; linear canonical transformations; quadratic operators; and Thirring's four-fermion model. State spaces and the simplest operators are also described. This book is comprised of four chapters and begins with an overview of the method of second quantization and the relevant notations. The first chapter focuses on the connections between vectors and functionals and between operators and functionals, together with fundamental rules for operating on functionals. The reader is then introduced to the so-called quadratic operators and the linear canonical transformations closely connected with them. Quadratic operators reduced and not reduced to normal form are considered. The final chapter discusses the Thirring model, the simplest relativistically invariant model in quantum field theory, and explains why it includes infinities. This monograph will be of value to students and practitioners of mathematical physics. Content: Pure and Applied Physics: A Series of Monographs and Textbooks Pages i-ii Front Matter Page iii Copyright page Page iv Preface to the English Edition Page v F.A. BEREZIN Preface Pages vii-ix F.A. BEREZIN Introduction Pages 1-8 Chapter I - Generating Functionals Pages 9-86 Chapter II - Linear Canonical Transformations Pages 87-132 Chapter III - Quadratic Operators Pages 133-180 Chapter IV - Thirring's Model in Quantum Field Theory Pages 181-202 Appendix: Wick's Theorem Pages 203-222 References Pages 223-226 Index Pages 227-228 By F.a. Berezin. Translated By Nobumichi Mugibayashi And Alan Jeffrey. Includes Index. Bibliography: P. 223-226.