Master · 1st year · 2025/26
Interacting Quantum Fields
Lecture notes in Cambridge style · 597 pages · Bjorken–Drell conventions with systematic Mandl–Shaw cross-checks.
Prerequisites & method
How the course is taught
Solid background in non-relativistic quantum mechanics, classical electrodynamics, special relativity and Lagrangian field theory. The course adopts the Bjorken–Drell normalization throughout, with systematic cross-checks against Mandl–Shaw conventions, and emphasizes deriving every formula from first principles rather than quoting results.
The lectures are organized in five parts that take the student from canonical free-field quantization, through the perturbative apparatus of QED, up to its renormalization, the LSZ formalism, and a self-contained introduction to supersymmetry.
Companion textbooks
- Peskin & Schroeder, An Introduction to Quantum Field Theory (Westview, 1995) — modern standard reference; Ch. 4–6 for QED, Ch. 10 for renormalization, Ch. 16 for the RG.
- Mandl & Shaw, Quantum Field Theory, 2nd ed. (Wiley, 2010) — the conventions adopted in these notes; Ch. 7–9.
- Schwartz, Quantum Field Theory and the Standard Model (Cambridge, 2014) — pedagogical modern treatment.
- Srednicki, Quantum Field Theory (Cambridge, 2007) — concise alternative, freely available online.
- Weinberg, The Quantum Theory of Fields, Vol. I (Cambridge, 1995) — rigorous foundations; Ch. 10 for LSZ.
- Bjorken & Drell, Relativistic Quantum Fields (McGraw–Hill, 1965) — classical reference for the conventions.
Programme
Five parts, from free-field quantization to supersymmetry.
Part I · Foundations of Quantum Field Theory
Ch. 1 · Free fields: a recap. Real and complex scalar fields; Klein–Gordon equation; mode expansion and canonical commutation relations; the Dirac field, spinors and anticommutators; the photon field, gauge fixing (Coulomb, Lorenz, Feynman) and the Gupta–Bleuler formalism; Feynman propagators; Noether’s theorem and conserved currents; comparison of normalization conventions.
Ch. 2 · Pictures of quantum dynamics. Schrödinger, Heisenberg and interaction (Dirac) pictures; unified framework and exponential evolution operators.
Ch. 3 · The Dyson series. Time ordering and the time-ordered exponential; definition of the S-matrix; cross sections in the Bjorken–Drell conventions.
Ch. 4 · Feynman rules. Perturbative expansion of the S-matrix; Wick’s theorem; $\lambda\phi^4$ theory as a warm-up; Feynman rules for QED in configuration and momentum space; the fermion minus sign.
Part II · Quantum Electrodynamics
Ch. 5 · QED scattering processes. The QED interaction vertex and classification of tree-level processes; muon pair production $e^+e^- \to \mu^+\mu^-$ with helicity considerations; Bhabha scattering; Compton scattering and the Klein–Nishina formula; scattering by an external field, the Mott formula and the Rutherford limit; bremsstrahlung, the soft-photon approximation, the infrared divergence and the Bloch–Nordsieck theorem.
Featured calculation: the unpolarized cross section for $e^+e^- \to \mu^+\mu^-$ is derived in full detail, then re-derived in the helicity basis to expose the chirality structure of QED.
Part III · Renormalization
Ch. 6 · Renormalization in QED. Warm-up on $\lambda\phi^4$ theory; photon self-energy (vacuum polarization); electron propagator renormalization; one-loop vertex correction; external line renormalization; the systematic renormalization programme of QED; power counting and the superficial degree of divergence; Wilson’s renormalization group, effective field theories and accidental symmetries.
Ch. 7 · Explicit calculations. Derivation of the finite parts in dimensional regularization — photon self-energy, electron self-energy, one-loop vertex correction; numerical size of one-loop QED corrections and phenomenological evidence (electron $g-2$, Lamb shift).
Ch. 8 · General methods for interacting fields. Properties of physical states; in- and out-fields, the asymptotic condition and the S-matrix; the spectral representation; the LSZ reduction formula for scalar and Dirac fields; Green’s functions and the S-matrix.
Part IV · Supersymmetry
Ch. 9 · Poincaré and Lorentz symmetries. The Lorentz group and its Lie algebra; the Poincaré group; spin-½ representations of the Lorentz group; bilinear covariants; four-component spinors and Lagrangians for free spin-½ fermions.
Ch. 10 · Introduction to supersymmetry. Why SUSY still matters — LHC null results, the Higgs at 125 GeV, the WIMP story; two-component spinor conventions; the free Wess–Zumino model; the SUSY algebra and supermultiplets (chiral and vector); interactions and the superpotential.
References: Wess & Bagger, Supersymmetry and Supergravity (Princeton, 1992); Martin, A Supersymmetry Primer (arXiv:hep-ph/9709356).
Part V · Appendices — the technical toolkit
A. Dirac gamma matrices · B. Choice of representation for Dirac matrices · C. Weyl spinor identities · D. Mandelstam variables · E. Single-spin projectors and helicity · F. Special functions for loop integrals · G. Feynman-integral technology.
The course in practice
Hours, period and examination, as the syllabus fixes them.
The examination is a single oral test. What is assessed is an adequate comprehension and an overall command of the concepts and arguments developed during the course — not the recollection of individual results.
By the end you are expected to understand what an interaction between fields is and to implement it in different physical models; to move through a quantum field theory on your own; to state what you have understood in the language of the subject; and to carry on studying from textbooks and from the literature without a course to follow.
Class material and communications
Interacting Quantum Fields — the book
The whole course in a single continuous book of 597 pages, with the prerequisite recap on free fields and the appendices alongside it. This is the material to read, whichever year you took the course. Direct downloads — no account, no sign-in.
The lectures as given
The twenty lectures of AA 2025/2026 as separate PDFs, in the order they were given, dated, with the topics covered in each. Kept apart from the book because they follow that year’s calendar: when the course runs again the notes are revised and the list is replaced.
Contact me by email for any clarification or to arrange a meeting: antonio.marrone@ba.infn.it · antonio.marrone@uniba.it.