Quantum field theory is the theory of many-particle quantum systems. Just as quantum mechanics describes a single particle as both a particle and a wave, quantum field theory describes many-particle systems in terms of both particles and fields. The study of phase transitions using field theory has become a unifying theme across most areas of physics. This second volume explores gauge theories and the renormalization group, with subsequent introductions to large-N methods, solitons and instantons, anomalies and finite-temperature field theory. Methods for the determination of the phase structure of field theories is a key theme of this book. This volume builds on the first and includes more references to original literature whilst exploring the central role field theory plays in modern physics. Graduate students studying particle, nuclear, and condensed matter physics are the key audience for this volume.
Key features:
- Emphasizes key concepts and techniques of field theory common across particle physics, nuclear physics, condensed matter
physics and cosmology.
- Examples and problems from many areas of modern physics.
- Each chapter includes worked examples and exercises within the main body of the text, with more substantial problems at the
end of each chapter.
Author(s): Michael Ogilvie
Edition: 1
Publisher: IOP
Year: 2022
Language: English
Pages: 154
Tags: Quantum Field Theory, Gauge Theories, Renormalization Group, Solitons, Instantons
PRELIMS.pdf
Preface from volume 1
Quantum field theory is ubiquitous in modern physics
What should be taught and who learns it is changing
How to use this book
Acknowledgements
Preface for volume 2
Acknowledgements
Author biography
Michael Ogilvie
CH001.pdf
Chapter 1 Gauge theories
1.1 Introduction to quantum electrodynamics
1.1.1 The massive spin-one field
1.1.2 The massless spin-one field
1.1.3 Unphysical states and the Coulomb force
1.2 Abelian gauge invariance
1.2.1 Functional integration and Abelian gauge invariance
1.3 Perturbative calculations at tree level in QED
1.4 Renormalization of QED
1.4.1 Renormalization of the photon and electron propagators
1.4.2 Renormalization of the vertex and the Ward–Takahashi identity
1.4.3 Vacuum polarization at one loop
1.5 Compact Lie groups
1.6 Non-Abelian gauge theories
1.7 The Faddeev–Popov ansatz and gauge fixing for non-Abelian gauge theories
1.8 The geometry of gauge fields
1.9 Gauge fields compared to gravity
1.10 The Feynman rules for non-Abelian gauge theories
1.11 The Higgs mechanism
1.11.1 The Abelian Higgs mechanism
1.11.2 The non-Abelian Higgs mechanism
1.11.3 The Glashow–Salam–Weinberg electroweak model
Problems
CH002.pdf
Chapter 2 The renormalization group
2.1 Introduction
2.2 The Ising model
2.3 The order parameter and Landau theory
2.4 Critical exponents
2.5 The real-space renormalization group
2.5.1 A thought experiment
2.5.2 Kadanoff block spins
2.5.3 An exact renormalization group in d = 1
2.5.4 The Migdal–Kadanoff renormalization group
2.6 Euclidean field theory
2.7 Derivation of the renormalization group equations: ϕ4
2.8 The Wilson–Fisher fixed point
2.9 The effective action
2.10 Background field method for scalar field theories
2.11 The background field method for gauge theories
Appendix: simulation and the Metropolis algorithm
Simulation of the two-dimensional Ising model
Measurements
Pitfalls
Application to quantum field theory
Problems
References
CH003.pdf
Chapter 3 The 1/N expansion
3.1 Introduction
3.2 Quantum mechanics
3.3 Vector models in quantum mechanics
3.4 Vector models in quantum field theory
3.5 Matrix models in the large-N limit
Problems
References
CH004.pdf
Chapter 4 Solitons and instantons
4.1 Introduction
4.2 The ϕ4 kink in 1 + 1 dimensions
4.3 Flux tubes
4.4 Magnetic monopoles
4.5 Instantons
4.5.1 The anharmonic oscillator
4.6 False vacuum decay
Problems
References
CH005.pdf
Chapter 5 Anomalies
5.1 Introduction
5.2 Path integral treatment of anomalies
5.3 Anomaly cancellation in gauge theories
5.4 The η′ problem and the U(1)A anomaly in QCD
Problems
References
CH006.pdf
Chapter 6 Field theory at nonzero temperature
6.1 Introduction
6.2 Partition functions and path integrals
6.3 Free fields and Matsubara frequencies
6.4 Evaluation of the T≠0 scalar field effective potential
6.5 Symmetry restoration
6.6 Running couplings
6.7 Fermions
6.8 Equilibration in field theories
Problems
References
