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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.
Preface to the English Edition
Chapter I. Generating Functionals
1. Creation and Annihilation Operators. Generating Functionals
2. Operations on Generating Functionals. Bose Case
3. Operations on Generating Functionals. Fermi Case
Chapter II. Linear Canonical Transformations
4. Bose Case
5. Fermi Case
Chapter III. Quadratic Operators
6. Quadratic Operators Reduced to Normal Form
7. Quadratic Operators Not Reduced to Normal Form
8. Canonical Form of a Quadratic Operator
Chapter IV. Thirring's Model in Quantum Field Theory
9. Thirring's Four-Fermion Model
Appendix. Wick's Theorem
- No. of pages:
- © Academic Press 1966
- 1st January 1966
- Academic Press
- eBook ISBN: