III: Quantum Mechanics in Fock Space

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This volume gives an introduction to the second-quantization description of non-relativistic many-body systems. This description is the standa¡d language of condensed matter physics and of low-energy nuclear physics. The quantum mechanics of a system of identical particles is conside¡ed in Chapter 2 and occupation number representation for systems of fermions and bosons is discussed in Chapter 3. The Fock space description of a system of identical fermions is given in Chapters 4 and 5. Chapter 4 contai¡s a derivation of the Ha¡tree-Fock potential and a description of correlated particle-hole sates of an r¿-fermion system. Quantum fields for fermions are introduced in Chapter 5. The Fock space description of the quantum mechanics of a system of identical bosons is given in Chapter 6. Quantum fields for bosons are introduced in this chapter. A system of fermions and bosons in inte¡action is conside¡ed in Chapter 7. This chapter includes the dressing transfo¡mation method for expressing the Hamiltonian of the system in te¡ms of ope¡ators for physical particles. The 'v'ukawa potential for interacting physical fermions is

Thumbnail: Pictorial representation of a Fock space. The initial empty box is the vacuum state. Each color represents a certain mode, a possible state for the particles. The black arrows mean creation of particles, and the white ones annihilation. The upper crossed out box represents the zero state (not to be confused with the vacuum). Image used with permission (GNU v.3 Lesser; David Vignoni).