Module 2 · The Field-Theoretic Core
QFT, Anomalies & Symmetries
Quantum field theory is the language of the Standard Model, of condensed-matter physics, and of much of cosmology. Several Dirac Medals have honoured discoveries in QFT itself — how it must be modified by quantum effects (anomalies), how its symmetries can be hidden or extended, and how new symmetries explain the absence of certain otherwise-allowed processes. The four lectures here survey those threads.
Stephen Adler — Numerical Integration in High Dimensions
Stephen Adler (Dirac Medal 1998, shared with John S. Bell) discovered the Adler–Bell–Jackiw axial anomaly in 1969 — the first concrete demonstration that a classical symmetry (chiral symmetry of massless fermions) can be broken by quantum effects. The anomaly explains the rate of \( \pi^0 \to \gamma\gamma \) decay, drives baryon-number non-conservation in the electroweak theory, and constrains every gauge theory ever written down. In this lecture Adler turns to a different problem — localising high-dimensional numerical integration by recursive 2psubdivision.
Stephen Adler — Localising Numerical Integration, Part 1
Adler reformulates high-dimensional Monte Carlo integration via a 2ᵖ-subdivision scheme that controls error locally rather than globally — with applications to lattice gauge theory and many-body physics.
Stephen Adler — Localising Numerical Integration, Part 2
Comparison with adaptive Monte Carlo and quasi-Monte Carlo schemes, and convergence analysis of the recursive subdivision in p dimensions.
Roman Jackiw — Fractional Charge & Majorana Fermions
Roman Jackiw (Dirac Medal 1998, shared with Adler and Bell) is, with Adler and Bell, the third name on the axial anomaly. He also discovered (with Rebbi) that fermion zero modes on topological solitons carry fractional fermion number — an insight later realised in the polyacetylene chain (Su–Schrieffer–Heeger model) and in modern condensed-matter realisations of Majorana fermions in superconducting topological wires (Kitaev, 2001).
Roman Jackiw — Fractional Charge & Majorana Fermions, Part 1
The Jackiw–Rebbi mechanism: fermion zero modes on a kink generate states with charge ±1/2. Connection to the SSH polyacetylene chain.
Roman Jackiw — Fractional Charge & Majorana Fermions, Part 2
Majorana zero modes at vortex cores in 2D p-wave superconductors and on the ends of 1D topological superconducting wires — the Kitaev chain — and their non-Abelian statistics.
John Iliopoulos — New Physics at the LHC
John Iliopoulos (Dirac Medal 2007, shared with Luciano Maiani) is the “I” of the GIM mechanism: the 1970 Glashow, Iliopoulos, Maiani argument that flavour-changing neutral currents are absent in the Standard Model only because of the existence of a fourth quark — the charm, predicted on this basis and discovered four years later. The lecture previews what the LHC could find beyond the Standard Model.
John Iliopoulos — New Physics at the LHC, Part 1
The status of the Standard Model on the eve of the LHC era: GIM, the role of the charm quark, and the hierarchy and naturalness puzzles that motivate beyond-SM searches.
John Iliopoulos — New Physics at the LHC, Part 2
Supersymmetric and extra-dimensional candidates for new physics at TeV energies, and the experimental signatures that could distinguish them.
Helen Quinn — Scale Hierarchies
Helen Quinn (Dirac Medal 2000) is best known for the Peccei–Quinn symmetry (1977, with Roberto Peccei) — an additional U(1) symmetry that, when spontaneously broken, naturally explains why the QCD vacuum angle \(\bar\theta\)is so small. The associated Goldstone boson is the axion, still a leading dark-matter candidate.
Helen Quinn — Scale Hierarchies, Part 1
The strong CP problem, the Peccei–Quinn solution, and how the axion mass and couplings are set by the scale of PQ symmetry breaking.
Helen Quinn — Scale Hierarchies, Part 2
Wider scale hierarchies in particle physics — gauge coupling unification, the QCD scale, the electroweak scale, neutrino masses — and what each tells us about high-energy completions of the Standard Model.