Introduction to Green's Function Methods in Many-Body Physics With Applications to Quantum Transport
Book contents
- Frontmatter
- Contents
- Abbreviations and Frequent Notations
- Preface
- Part I Preliminaries
- 1 Second Quantisation Ignoring Spin
- 2 Second Quantisation via Relativistic Treatment of Many Electrons
- 3 Operators, Interactions, Hamiltonians, Mean Field and Linear Response
- Part II Equilibrium
- Part III Non-equilibrium
- Part IV Quantum Transport Applications
- Appendix A Non-Hermitian Hamiltonian
- Appendix B Angular Momentum of an Electron
- Appendix C Canonical Transformation
- Appendix D The Delta Function
- References
- Index
1 - Second Quantisation Ignoring Spin
from Part I - Preliminaries
Published online by Cambridge University Press: aN Invalid Date NaN
Book contents
- Frontmatter
- Contents
- Abbreviations and Frequent Notations
- Preface
- Part I Preliminaries
- 1 Second Quantisation Ignoring Spin
- 2 Second Quantisation via Relativistic Treatment of Many Electrons
- 3 Operators, Interactions, Hamiltonians, Mean Field and Linear Response
- Part II Equilibrium
- Part III Non-equilibrium
- Part IV Quantum Transport Applications
- Appendix A Non-Hermitian Hamiltonian
- Appendix B Angular Momentum of an Electron
- Appendix C Canonical Transformation
- Appendix D The Delta Function
- References
- Index
Summary
This chapter is devoted to introducing the second quantisation, a language that is alternative to using wave functions; we shall deal with many-body states in the Fock space, characterised by particles that occupy them. Ignoring spin here, we shall start from the first quantisation by showing that the many-body wave function is expanded in Slater determinants (permanents) and will derive Slater rules for matrix elements between such many-body basis functions. Then second quantisation is defined by setting an identity relationship (a map) between the states and the Slater determinants. Next one- and two-particle interactions in the second quantisation are defined such that results identical to the Slater rules of the first quantisation are guaranteed.
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- Introduction to Green's Function Methods in Many-Body PhysicsWith Applications to Quantum Transport, pp. 3 - 27Publisher: Cambridge University PressPrint publication year: 2026
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