- 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

# Statistical field theory

# Statistical field theory

- Chapter:
- (p.228) 25 Statistical field theory
- Source:
- Quantum Field Theory for the Gifted Amateur
- Author(s):
### Tom Lancaster

### Stephen J. Blundell

- Publisher:
- Oxford University Press

There is a rather subtle connection between quantum field theory and statistical physics, and this is explored here, where the concepts of imaginary time and the Wick rotation are introduced.

*Keywords:*
statistical field theory, imaginary time, Wick rotation

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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