Field Theory Lecture Notes

John Preskill

These are scanned handwritten lecture notes for courses I have taught on particle theory, field theory, and scattering theory.


Physics 230abc, Quantum Chromodynamics, 1983-1984

Chapter 1, Introduction to quantum chromodynamics
pages 1-9 + more : QCD, renormalization, power counting and renormalizability, universality, running coupling constant
pages 10-69 : renormalization group, fixed points, dimensional regularization, beta function, anomalous dimension, critical phenomena, composite operators, operator product expansion, LSZ reduction formula, QED beta function, path integral
pages 70-113 : quantization of gauge theories, background field method in Yang-Mills theory, asymptotic freedom, e+e- annihilation to hadrons, quarkonium decay, infrared divergences and jets
pages 114-174 : infrared divergences and jets continued, electroproduction and parton model, structure functions of proton and photon, heavy quarks, semi-inclusive and exclusive processes, effective weak-interaction Hamiltonian

Chapter 2, Quark confinement (see “Phases of Gauge Theories” here for an updated discussion)
pages 1-35 : strings and vortices, Wilson loop and area-law criterion for confinement, magnetic disorder, confinement in 2+1 and in 3+1 dimensions, twisted gauge fields in a box
pages 36-63 : electric-magnetic duality relations, deconfinement at finite temperature, dynamical quarks, indistinguishability of Higgs and confinement phases, finite temperature and dynamical quarks

Chapter 3, Chiral symmetry
pages 1-22 + more : pair condensation and spontaneous breakdown of chiral symmetry, constituent and current quark masses, restoration of chiral symmetry at finite temperature, chiral Lagrangians and chiral perturbation theory, chiral anomaly in two and four dimensions as chiral pair production in electromagnetic fields, vector and axial Ward identities, anomalies and massless particles
pages 23-74 : triangle diagram, no higher-loop radiative corrections to anomaly, operator and path integral derivations, Atiyah-Singer index theorem, neutral pion decay, instantons and the U(1) problem, theta parameter, chiral selection rule
pages 75-117 : anomalies in nonabelian gauge theories, ‘t Hooft anomaly condition, chiral symmetry breaking in QCD, chiral gauge theories,
pages 118-149 : trace anomaly, nonperturbative SU(2) anomaly, magnetic monopole, Wess-Zumino consistency condition
supplement : Differential geometry and chiral anomalies, Green-Schwarz anomaly cancellation, Wess-Zumino effective Lagrangian, topological interpretation of nonabelian anomalies, chiral solitons (lecture by H. Sonoda)

Chapter 4, The large-N limit
pages 1-46: Gross-Neveu model, quasi-long-range order, planar diagrams in QCD, mesons and glueballs, eta-prime mass, baryons

Chapter 5, Lattice gauge theory
pages 1-55: Wilson action, Haar measure, strong-coupling expansion, roughening, mass gap, duality in Z2 theory, Wilson and ‘t Hooft loops, phase diagrams

Physics 236c, Quantum Field Theory in Curved Spacetime, 1990

Chapter 0, Introduction
pages 1-10
Chapter 1, Quantum field theory in flat spacetime
pages 1-38 : irreps of Poincare group, relativistic causality, positive and negative frequencies, canonical quantization
Chapter 2, Quantum field theory on curved spacetime
pages 1-40 : free scalar field on globally hyperbolic spacetime, Bogoliubov transformation and S-matrix
Chapter 3, Quantum field theory on Rindler spacetime
pages 1-35 : uniformly accelerated particle detector, Rindler coordinates for Minkowski spacetime, Unruh radiation
pages 36-70 : uniformly accelerated charged particle, thermal Green functions as analytic functions 
Chapter 4, Black Hole Radiance
pages 1-40 : Schwarzschild geometry, Kruskal coordinates, scalar field on Schwarzschild geometry, spherically symmetric collapsing star
pages 41-80 : Hawking radiation, Boulware and Unruh vacuum states, Kerr black hole, black hole thermodynamics
pages 81-126 : Hartle-Hawking state, renormalized stress-energy tensor in flat and curved spacetime, black hole evaporation

Physics 205abc, Quantum Field Theory, 1986-87

Chapter 0, Introduction and Table of Contents

pages 1-12


Chapter 1, The free scalar field

pages 1-45: canonical quantization, Lorentz group, causality, measurement of quantum fields

pages 46-87: symmetries and conservation laws, Wightman axioms, CPT theorem


Chapter 2, Interacting scalar fields

pages 1-49 : interaction picture, S-matrix, Wick’s theorem, Feynman rules, vacuum energy

pages 50-102 : reaction rates, crossing symmetry, unitarity, dispersion relations, resonances, mass and field renormalization

pages 103-155 : renormalizability, universality, loop diagrams, Green functions, asymptotic condition and S-matrix


Chapter 3, Spin 1/2

pages 1-53 : Unitary irreps of Poincare group, spin and statistics, free Weyl and Dirac fermions

pages 54-111 : Dirac equation, hole theory, discrete symmetries, Feynman rules for fermions


Chapter 4, Functional integration

pages 1-63 : path integral, semiclassical expansion, derivative interactions, effective action, Ward identities


Chapter 5, Quantum electrodynamics

pages 1-51: free vector field, axial gauge, Faddeev-Popov ansatz, Feynman rules

pages 52-121: elementary processes, loops, dimensional regularization, running coupling constant, infrared divergences, anomalous magnetic moment


Chapter 6, Spontaneous symmetry breakdown

pages 1-43: vacuum degeneracy, Goldstone bosons, current algebra

pages 44-82: charged weak current, pion and neutron decay, interactions of Goldstone bosons, Higgs mechanism


Chapter 7, Nonabelian gauge fields and the standard model

pages 1-35: geometry of gauge fields, nonabelian Higgs mechanism, model of leptons

pages 35-71: decays of W, Z, and Higgs boson, GIM mechanism, new physics

Physics 230bc, Field Theory and Topology, 2000

For more detailed summaries of the lectures and problem sets, see the course home page here.

Part I:  Vortices and Anyons

Lectures 1-6, pages 1-53: Geometry of gauge fields (notes on this are kind of sketchy), abelian Higgs model and vortices, local discrete symmetry, anyons, abelian Chern-Simons theory, fractional quantum Hall effect

Lectures 7-10, pages 53-109 : Topological degeneracy, quantization of Chern-Simons theory, lifting of topological degeneracy, nonlinear sigma model and skyrmions, Alice strings and Cheshire charge

Lectures 11-13, pages 109-152 : Vortices as nonabelian anyons, Aharonov-Bohm scattering, holonomy interactions of strings, magnetic monopoles and Dirac quantization condition

Part II:  Monoples, Dyons, and Instantons

Lectures 14-17, pages 153-206 : Monopoles as topological solitons, upper bound on monopole and dyon mass, moduli-space approximation, magnetic charge and exact homotopy sequence, grand-unified monopoles, magnetically charged black holes

Lectures 18-20, pages 207-251: Magnetic Cheshire charge, Strings ending on monopoles, walls bounded by strings, topological classification of gauge fields, cohomology with integer coefficients, U(1) bundles, first Chern class, torsion classes, flat connections on nonorientable manifolds, G-bundles

Lectures 21-23, pages 252-298: Spin manifolds and second Stiefel-Whitney class, spin structures on coset manifolds, Berry phase, quantization of Hall conductivity, stable homotopies, second Chern class, semiclassical physics and instantons, dilute instanton gas approximation, decay of unstable states and the “bounce” solution, decay of unstable solitons, beads on strings

Lectures 24-26, pages 299-346: Yang-Mills theory and its quantization, theta vacua and CP nonconservation, theta-dependent dyon charge, nonabelian monopoles and global gauge transformations


Part III:  Phases of Gauge Theories


Lectures 27-29, pages 347-402: Realizations of global symmetries and local order parameters, Wilson loop and area law criterion for confinement, magnetic disorder, abelian Higgs model in 1+1 and 2+1 dimensions, magnetic monopoles as instantons in 2+1 dimensions, spontaneous breakdown of Z_N global symmetry in SU(N) Yang-Mills theory

Lectures 30-31, pages 403-441: The ‘t Hooft loop operator, magnetic and electric confinement in (3+1)-dimensional Yang-Mills theory, electric-magnetic duality, deconfinement at finite temperature and realization of ZN global symmetry, dynamical quarks and absence of confinement-Higgs phase boundary


Part IV: Anomalies


Lecture 32, pages 1-13: Chiral anomaly in two and four dimensions as chiral pair production in electromagnetic fields, vector and axial Ward identities, anomalies and massless particles

Lectures 33-34, see “Chiral symmetry” here: Chiral anomalies from path integral viewpoint, heat kernel expansion and Atiyah-Singer index theorem, U(1) problem, axion, ‘t Hooft anomaly condition, unbroken chiral symmetry in supersymmetric QCD

Physics 164, Scattering Theory, 1982

Chapters 1-3

Chapter 1, Quantum Mechanics: states, observables, measurements, dynamics, spectra

Chapter 2, Time-Dependent Scattering Formalism: asymptotic states, wave operators, S-matrix, cross section, optical theorem

Chapter 3, Analytic functions: derivative, integrals, power series, residue theorem, analytic continuation, Riemann surfaces

Chapters 4-5

Chapter 4: Time-Independent Scattering Formalism: Green’s operator, wave operators, Lippmann-Schwinger equation, S-matrix, stationary scattering states,

Chapter 5, Methods of Approximation: Born series, Born approximation, convergence, Yukawa potential, Fredholm method, quasiparticle method

Chapter 6

Chapter 6, Partial-Wave Expansion: central potential, partial-wave scattering states, partial-wave amplitude, regular solution, Jost function, analytic continuation, Levinson’s theorem, threshold behavior, resonance poles and second sheet, time delay and exponential decay

Chapters 7-8

Chapter 7, Complex Angular Momentum and Regge Poles: analytic continuation in angular momentum, Regge poles, Coulomb potential, Sommerfeld-Watson transform, Regge poles in relativistic scattering, Froissart bound

Chapter 8, Dispersion Relations: forward amplitude, partial-wave dispersion relations, nonzero momentum transfer, fixed energy, Mandelstam representation

Chapter 9

Chapter 9, Multichannel Scattering: channels, off-shell T-matrix, Born approximation, target-state expansion and coupled channels, analyticity of multichannel S-matrix, resonances, final-state interactions

Other miscellaneous notes

Typed notes on quantum computing. See also handwritten updates here.
Notes on noise, December 2006.

Vortices and Monopoles, Les Houches Summer School Lectures, 1985.

Introduction to general relativity and cosmology (Ph 136c, 1998).
Part 1 (pages 1-35): differential geometry, tensors, covariant derivative, parallel transport, geodesics.
Part 2 (pages 36-70): curvature, Bianchi identities, geodesic deviation, Einstein field equations, graviational waves.
Part 3 (pages 71-111): relativistic cosmologies, cosmic microwave background radiation, nucleosynthesis, CMB anisotropy.

Introduction to dynamical systems and Hamiltonian chaos (Ph 106b, 1994).
Part 1 (pages 1-18): Sensitive dependence on initial conditions, Poincare section, tent map and shift map.
Part 2 (pages 19-34): Baker’s map, cat map, chaotic billiards, logistic map, Lyapunov exponents.
Part 3 (pages 35-57): Integrable Hamiltonian dynamics, invariant tori, canonical perturbation theory, KAM theorem.
Part 4 (pages 58-79): Poincare-Birkhoff theorem, fixed points, rational torus destruction, homoclinic tangle.