- Title Pages
- Preface
- 0 Overture
- Part I The Universe as a set of harmonic oscillators
- 1 Lagrangians
- 2 Simple harmonic oscillators
- 3 Occupation number representation
- 4 Making second quantization work
- Part II Writing down Lagrangians
- 5 Continuous systems
- 6 A first stab at relativistic quantum mechanics
- 7 Examples of Lagrangians, or how to write down a theory
- Part III The need for quantum fields
- 8 The passage of time
- 9 Quantum mechanical transformations
- 10 Symmetry
- 11 Canonical quantization of fields
- 12 Examples of canonical quantization
- 13 Fields with many components and massive electromagnetism
- 14 Gauge fields and gauge theory
- 15 Discrete transformations
- Part IV Propagators and perturbations
- 16 Propagators and Green’s functions
- 17 Propagators and fields
- 18 The <i>S</i>-matrix
- 19 Expanding the <i>S</i>-matrix: Feynman diagrams
- 20 Scattering theory
- Part V Interlude: wisdom from statistical physics
- 21 Statistical physics: a crash course
- 22 The generating functional for fields
- Part VI Path integrals
- 23 Path integrals: I said to him, ‘You’re crazy’
- 24 Field integrals
- 25 Statistical field theory
- 26 Broken symmetry
- 27 Coherent states
- 28 Grassmann numbers: coherent states and the path integral for fermions
- Part VII Topological ideas
- 29 Topological objects
- 30 Topological field theory
- Part VIII Renormalization: taming the infinite
- 31 Renormalization, quasiparticles and the Fermi surface
- 32 Renormalization: the problem and its solution
- 33 Renormalization in action: propagators and Feynman diagrams
- 34 The renormalization group
- 35 Ferromagnetism: a renormalization group tutorial
- Part IX Putting a spin on QFT
- 36 The Dirac equation
- 37 How to transform a spinor
- 38 The quantum Dirac field
- 39 A rough guide to quantum electrodynamics
- 40 QED scattering: three famous cross-sections
- 41 The renormalization of QED and two great results
- Part X Some applications from the world of condensed matter
- 42 Superfluids
- 43 The many-body problem and the metal
- 44 Superconductors
- 45 The fractional quantum Hall fluid
- Part XI Some applications from the world of particle physics
- 46 Non-abelian gauge theory
- 47 The Weinberg–Salam model
- 48 Majorana fermions
- 49 Magnetic monopoles
- 50 Instantons, tunnelling and the end of the world
- A Further reading
- B Useful complex analysis
- Index

# Occupation number representation

# Occupation number representation

- Chapter:
- (p.28) 3 Occupation number representation
- Source:
- Quantum Field Theory for the Gifted Amateur
- Author(s):
### Tom Lancaster

### Stephen J. Blundell

- Publisher:
- Oxford University Press

This chapter changes our viewpoint and get rid of wave functions entirely and develops the occupation number representation. The chapter shows that bosons are described by commuting operators and fermions are described by anticommuting operators.

*Keywords:*
occupation number representation, bosons, fermions, second quantization, indistinguishability

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- Title Pages
- Preface
- 0 Overture
- Part I The Universe as a set of harmonic oscillators
- 1 Lagrangians
- 2 Simple harmonic oscillators
- 3 Occupation number representation
- 4 Making second quantization work
- Part II Writing down Lagrangians
- 5 Continuous systems
- 6 A first stab at relativistic quantum mechanics
- 7 Examples of Lagrangians, or how to write down a theory
- Part III The need for quantum fields
- 8 The passage of time
- 9 Quantum mechanical transformations
- 10 Symmetry
- 11 Canonical quantization of fields
- 12 Examples of canonical quantization
- 13 Fields with many components and massive electromagnetism
- 14 Gauge fields and gauge theory
- 15 Discrete transformations
- Part IV Propagators and perturbations
- 16 Propagators and Green’s functions
- 17 Propagators and fields
- 18 The <i>S</i>-matrix
- 19 Expanding the <i>S</i>-matrix: Feynman diagrams
- 20 Scattering theory
- Part V Interlude: wisdom from statistical physics
- 21 Statistical physics: a crash course
- 22 The generating functional for fields
- Part VI Path integrals
- 23 Path integrals: I said to him, ‘You’re crazy’
- 24 Field integrals
- 25 Statistical field theory
- 26 Broken symmetry
- 27 Coherent states
- 28 Grassmann numbers: coherent states and the path integral for fermions
- Part VII Topological ideas
- 29 Topological objects
- 30 Topological field theory
- Part VIII Renormalization: taming the infinite
- 31 Renormalization, quasiparticles and the Fermi surface
- 32 Renormalization: the problem and its solution
- 33 Renormalization in action: propagators and Feynman diagrams
- 34 The renormalization group
- 35 Ferromagnetism: a renormalization group tutorial
- Part IX Putting a spin on QFT
- 36 The Dirac equation
- 37 How to transform a spinor
- 38 The quantum Dirac field
- 39 A rough guide to quantum electrodynamics
- 40 QED scattering: three famous cross-sections
- 41 The renormalization of QED and two great results
- Part X Some applications from the world of condensed matter
- 42 Superfluids
- 43 The many-body problem and the metal
- 44 Superconductors
- 45 The fractional quantum Hall fluid
- Part XI Some applications from the world of particle physics
- 46 Non-abelian gauge theory
- 47 The Weinberg–Salam model
- 48 Majorana fermions
- 49 Magnetic monopoles
- 50 Instantons, tunnelling and the end of the world
- A Further reading
- B Useful complex analysis
- Index