Quantum Field Theory

Path-Integral Essay
Schwartz QFT Solutions
Peskin & Schroeder QFT Solutions
David Tong Quantum Field Theory Solutions
David Tong Standard Model Solutions
PSI QFT II Solutions
Hugh Osborn AQFT Solutions
Mark Srednicki QFT Solutions
Independent φ³ Computation

Papers

I. Path Integrals and the Quantum–Statistical Correspondence Imperial Year-2 essay — Feynman's path integral, Wick rotation, and the partition function. HTML PDF Essay

Completed solutions to M. D. Schwartz’s Quantum Field Theory and the Standard Model Book website ↗

29. Chapter 29 — Weak interactions Completed Problems 29.1, 29.2, 29.3, 29.6, 29.7, 29.8, 29.9, collected in one chapter edition. HTML PDF 7 completed problems

Solutions to David Tong’s The Standard Model example sheets Original course ↗

I. Sheet 1: The Basics Weyl spinors, fermion masses, and discrete symmetries. Worked problems: 1, 2, 3, 4, 6, 7, 8. HTML PDF Tong Standard Model · Sheet 1
II. Sheet 2: Symmetry Breaking and QCD Goldstone modes, Higgs mechanisms, QCD running, and meson masses. Worked problems: 1, 2, 3, 4, 5, 6, 7, 8. HTML PDF Tong Standard Model · Sheet 2
III. Sheet 3: Anomalies Gauge anomalies, hypercharges, anomaly matching, and global symmetries. Worked problems: 1, 2, 3, 4, 5, 6. HTML PDF Tong Standard Model · Sheet 3
IV. Sheet 4: The Standard Model Running couplings, electric charges, flavour parameters, and two Higgs doublets. Worked problems: 1, 2, 4, 5, 6. HTML PDF Tong Standard Model · Sheet 4

Solutions to Peskin & Schroeder’s An Introduction to Quantum Field Theory Publisher page ↗

I. Equivalent Photon Approximation Peskin & Schroeder, Problem 6.2. HTML PDF Peskin Ch. 6
II. Alternative Regulators in QED Peskin & Schroeder, Chapter 7 — Pauli–Villars vs. dimensional regularization. HTML PDF Peskin Ch. 7
III. Final Project — Radiation of Gluon Jets Peskin & Schroeder, end-of-book project. HTML PDF Peskin Final

Solutions to David Tong’s Quantum Field Theory problem sheets Original course ↗

PS1. Lorentz, Symmetries & Currents \(\mathrm{SO}(3)\), infinitesimal Lorentz, energy-momentum tensor (incl. EM field), Proca, scale invariance. HTML PDF Tong PS1
PS2. Canonical Quantization & the Free Scalar String quantization, free scalar, normal ordering, Yukawa, Wick's theorem, Feynman propagator. HTML PDF Tong PS2
PS3. Dirac Field & Spin-Statistics Clifford algebra, Lorentz from \(\gamma\)-matrices, traces, plane-wave spinors, canonical quantisation. HTML PDF Tong PS3
PS4. Interactions & Tree-Level Amplitudes Wick's theorem at tree level — \(\phi^4\) 3-to-3, vacuum bubbles, Yukawa, Compton, \(e^-e^+\to\mu^-\mu^+\). HTML PDF Tong PS4

Perimeter Scholars International · Quantum Field Theory II

PS1. Correlation Functions in Quantum Mechanics Euclidean and real-time path-integral propagators of the harmonic oscillator at finite temperature. HTML PDF PSI QFT II · PS1
H1. Generating Functionals for \(\phi^4\) Theory Generating functionals, connected correlators, vacuum diagrams, and the 1PI effective action. HTML PDF PSI QFT II · Homework 1
H2. Renormalization in Massive \(\phi^4\) Theory Cutoff renormalization, running coupling and mass, and RG flow in the O(N) model. HTML PDF PSI QFT II · Homework 2
T3. Saddle-Point Approximation and Functional Determinants Saddle points, functional determinants, zeta regularization, and the Gel'fand-Yaglom formalism. HTML PDF PSI QFT II · Tutorial 3
T4. Exact Results in Quantum Field Theory The Källén-Lehmann representation, spectral functions, and Schwinger-Dyson equations. HTML PDF PSI QFT II · Tutorial 4
T5. Effective Action and Renormalization in \(\phi^3\) Theory The effective action, loop expansion, counterterms, and renormalization of \(\phi^3\) theory. HTML PDF PSI QFT II · Tutorial 5
T6. Renormalization-Group Flow in Three Dimensions Dimensionless couplings, beta functions, and the infrared fixed point of three-dimensional \(\phi^4\) theory. HTML PDF PSI QFT II · Tutorial 6
T7. Berezin Integration and the Gross-Neveu Model Grassmann Gaussian integrals, fermionic correlators, and large-N Gross-Neveu theory. HTML PDF PSI QFT II · Tutorial 7
T8. SU(N) Yang-Mills Theory and Scalar Fields Fundamental and adjoint representations, covariant derivatives, scalar couplings, and Yang-Mills zero modes. HTML PDF PSI QFT II · Tutorial 8
T9. The Faddeev-Popov Determinant Gauge-orbit volume, gauge slices, Jacobians, Gaussian gauge fixing, and ghost variables. HTML PDF PSI QFT II · Tutorial 9

Solutions to Hugh Osborn’s Advanced Quantum Field Theory example sheets Course materials ↗

O2. Functional Methods & Grassmann Integrals Osborn AQFT Example Sheet 2 — Legendre transform, 1PI effective action, Green's-function/vertex relations, Grassmann Gaussian integrals, Pfaffians, fermionic partition function, SUSY QM. (Q1–Q8) HTML PDF Osborn AQFT · ES2
O3. Feynman Graphs & RG Calculations Osborn AQFT Example Sheet 3 — superficial divergence, Feynman parameters, position-space loop integrals, \(\phi^4\) counter-terms, two-loop β functions, RG equations, \(\phi^3\) in \(d=6\). (Q1–Q10) HTML PDF Osborn AQFT · ES3

Solutions to Mark Srednicki’s Quantum Field Theory Author’s page ↗

S1. Nonabelian Symmetries Srednicki Ch. 24 — antisymmetry of the generator, structure constants from \(\mathrm{SO}(N)\), Noether current and charge algebra, generators of \(\mathrm{Sp}(2N)\). (Q24.1–24.4) HTML PDF Srednicki Ch. 24
S2. Renormalization Group for \(\phi\text{-}\chi\) Theory Srednicki Ch. 28 — one-loop Z-factors in MS-bar, \(\beta\)-functions for the \(\phi^3\) + \(\phi\chi^2\) couplings, and asymptotic freedom condition on \(h/g\). (Q28.3) HTML PDF Srednicki Ch. 28

Independent computation

I. Computation for \(\phi^3\) Theory Counter-terms, partition functional, and one-loop diagrams in \(\phi^3\) scalar theory; follows Srednicki and Peskin & Schroeder. HTML PDF \(\phi^3\)

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