Conceptual Framework of Quantum Field Theory
1st Edition
Published on 9. August 2012
793 pages
978-0-19-164220-3 (ISBN)
Description
The book provides a step by step construction of the framework of relativistic quantum field theory, starting from a minimal set of basic foundational postulates. The emphasis is on a careful and detailed description of the conceptual subtleties of modern field theory, many of which are glossed over in other texts.
More details
Other editions
Additional editions
Anthony Duncan
The Conceptual Framework of Quantum Field Theory
Book
08/2012
Oxford University Press
€214.00
Shipment within 15-20 days
Content
- Cover
- Contents
- 1 Origins I: From the arrow of time to the first quantum field
- 1.1 Quantum prehistory: crises in classical physics
- 1.2 Early work on cavity radiation
- 1.3 Planck's route to the quantization of energy
- 1.4 First inklings of field quantization: Einstein and energy fluctuations
- 1.5 The first true quantum field: Jordan and energy fluctuations
- 2 Origins II: Gestation and birth of interacting field theory: from Dirac to Shelter Island
- 2.1 Introducing interactions: Dirac and the beginnings of quantum electrodynamics
- 2.2 Completing the formalism for free fields: Jordan, Klein, Wigner, Pauli, and Heisenberg
- 2.3 Problems with interacting fields: infinite seas, divergent integrals, and renormalization
- 3 Dynamics I: The physical ingredients of quantum field theory: dynamics, symmetries, scales
- 4 Dynamics II: Quantum mechanical preliminaries
- 4.1 The canonical (operator) framework
- 4.2 The functional (path-integral) framework
- 4.3 Scattering theory
- 4.4 Problems
- 5 Dynamics III: Relativistic quantum mechanics
- 5.1 The Lorentz and Poincaré groups
- 5.2 Relativistic multi-particle states (without spin)
- 5.3 Relativistic multi-particle states (general spin)
- 5.4 How not to construct a relativistic quantum theory
- 5.5 A simple condition for Lorentz-invariant scattering
- 5.6 Problems
- 6 Dynamics IV: Aspects of locality: clustering, microcausality, and analyticity
- 6.1 Clustering and the smoothness of scattering amplitudes
- 6.2 Hamiltonians leading to clustering theories
- 6.3 Constructing clustering Hamiltonians: second quantization
- 6.4 Constructing a relativistic, clustering theory
- 6.5 Local fields, non-localizable particles!
- 6.6 From microcausality to analyticity
- 6.7 Problems
- 7 Dynamics V: Construction of local covariant fields
- 7.1 Constructing local, Lorentz-invariant Hamiltonians
- 7.2 Finite-dimensional representations of the homogeneous Lorentz group
- 7.3 Local covariant fields for massive particles of any spin: the Spin-Statistics theorem
- 7.4 Local covariant fields for spin-½ (spinor fields)
- 7.5 Local covariant fields for spin-1 (vector fields)
- 7.6 Some simple theories and processes
- 7.7 Problems
- 8 Dynamics VI: The classical limit of quantum fields
- 8.1 Complementarity issues for quantum fields
- 8.2 When is a quantum field "classical"?
- 8.3 Coherent states of a quantum field
- 8.4 Signs, stability, symmetry-breaking
- 8.5 Problems
- 9 Dynamics VII: Interacting fields: general aspects
- 9.1 Field theory in Heisenberg representation: heuristics
- 9.2 Field theory in Heisenberg representation: axiomatics
- 9.3 Asymptotic formalism I: the Haag-Ruelle scattering theory
- 9.4 Asymptotic formalism II: the Lehmann-Symanzik-Zimmermann (LSZ) theory
- 9.5 Spectral properties of field theory
- 9.6 General aspects of the particle-field connection
- 9.7 Problems
- 10 Dynamics VIII: Interacting fields: perturbative aspects
- 10.1 Perturbation theory in interaction picture and Wick's theorem
- 10.2 Feynman graphs and Feynman rules
- 10.3 Path-integral formulation of field theory
- 10.4 Graphical concepts: N-particle irreducibility
- 10.5 How to stop worrying about Haag's theorem
- 10.6 Problems
- 11 Dynamics IX: Interacting fields: non-perturbative aspects
- 11.1 On the (non-)convergence of perturbation theory
- 11.2 "Perturbatively non-perturbative" processes: threshhold bound states
- 11.3 "Essentially non-perturbative" processes: non-Borel-summability in field theory
- 11.4 Problems
- 12 Symmetries I: Continuous spacetime symmetry: why we need Lagrangians in field theory
- 12.1 The problem with derivatively coupled theories: seagulls, Schwinger terms, and T* products
- 12.2 Canonical formalism in quantum field theory
- 12.3 General condition for Lorentz-invariant field theory
- 12.4 Noether's theorem, the stress-energy tensor, and all that stuff
- 12.5 Applications of Noether's theorem
- 12.6 Beyond Poincaré: supersymmetry and superfields
- 12.7 Problems
- 13 Symmetries II: Discrete spacetime symmetries
- 13.1 Parity properties of a general local covariant field
- 13.2 Charge-conjugation properties of a general local covariant field
- 13.3 Time-reversal properties of a general local covariant field
- 13.4 The TCP and Spin-Statistics theorems
- 13.5 Problems
- 14 Symmetries III: Global symmetries in field theory
- 14.1 Exact global symmetries are rare!
- 14.2 Spontaneous breaking of global symmetries: the Goldstone theorem
- 14.3 Spontaneous breaking of global symmetries: dynamical aspects
- 14.4 Problems
- 15 Symmetries IV: Local symmetries in field theory
- 15.1 Gauge symmetry: an example in particle mechanics
- 15.2 Constrained Hamiltonian systems
- 15.3 Abelian gauge theory as a constrained Hamiltonian system
- 15.4 Non-abelian gauge theory: construction and functional integral formulation
- 15.5 Explicit quantum-breaking of global symmetries: anomalies
- 15.6 Spontaneous symmetry-breaking in theories with a local gauge symmetry
- 15.7 Problems
- 16 Scales I: Scale sensitivity of .eld theory amplitudes and effective field theories
- 16.1 Scale separation as a precondition for theoretical science
- 16.2 General structure of local effective Lagrangians
- 16.3 Scaling properties of effective Lagrangians: relevant, marginal, and irrelevant operators
- 16.4 The renormalization group
- 16.5 Regularization methods in field theory
- 16.6 Effective field theories: a compendium
- 16.7 Problems
- 17 Scales II: Perturbatively renormalizable field theories
- 17.1 Weinberg's power-counting theorem and the divergence structure of Feynman integrals
- 17.2 Counterterms, subtractions, and perturbative renormalizability
- 17.3 Renormalization and symmetry
- 17.4 Renormalization group approach to renormalizability
- 17.5 Problems
- 18 Scales III: Short-distance structure of quantum field theory
- 18.1 Local composite operators in field theory
- 18.2 Factorizable structure of field theory amplitudes: the operator product expansion
- 18.3 Renormalization group equations for renormalized amplitudes
- 18.4 Problems
- 19 Scales IV: Long-distance structure of quantum field theory
- 19.1 The infrared catastrophe in unbroken abelian gauge theory
- 19.2 The Bloch-Nordsieck resolution
- 19.3 Unbroken non-abelian gauge theory: confinement
- 19.4 How confinement works: three-dimensional gauge theory
- 19.5 Problems
- Appendix A: The functional calculus
- Appendix B: Rates and cross-sections
- Appendix C: Majorana spinor algebra
- References
- Index
- A
- B
- C
- D
- E
- F
- G
- H
- I
- J
- K
- L
- M
- N
- O
- P
- Q
- R
- S
- T
- U
- V
- W
- Y
- Z
