Lattice models to QFT (chain of oscillators with nearest neighbour interactions to scalar fields) [my notes, also [diF sec.2.1.1] [P sec.2.3]]; generalities on relativity + quantum mechanics to QFT [partly S ch.1, P ch.2]; relativistic scalar field, canonical quantization [S ch.3] [P ch.2]; propagators and causality [P sec.2.4]; spin statistics for scalar bosons [S ch.4];
Lorentz group Lie algebra and its representations [Sw 10.1-10.3] [S] [P]; fermions and spinor representations, Dirac equation [Sw 10.1-10.3] [P] [S]; spinors and Lorentz transformations [Sw 10.3].
LSZ reduction, scalar field theory [S ch.5] [P ch.4]; free field correlation functions via Feynman path integrals [S ch.8] [P ch.9]; path integrals for interacting phi^3 scalar field in perturbation theory [S ch.9]; scattering amplitudes, Feynman rules [S ch.10] [P 9.2-9.3]; tree amplitudes, Mandelstam variables, scattering and differential cross-sections (briefly) [S ch.11] [P 5.4]; loop amplitudes and divergences;
phi^4 scalar field theory and perturbative 1-loop renormalization, calculationally (Feynman parameters, dimensional regularization, Euclidean continuations, renormalized perturbation theory at 1-loop, fixing mass/coupling counterterms [P, 6.3, 7.5, 10.2]; field strength renormalization and a brief glimpse at the Kallen-Lehmann spectral representation [P 7.1].
Other regularization schemes [P 6.3, 7.1] [Sw 15.4, 16.1, App.B]: recall the 1-loop momentum integral by dim.reg.; then use Pauli Villars and evaluate via Euclideanizing; then differentiate under integral sign and evaluate, then integrate to obtain the log-regulator matching with Pauli-Villars.
Example [Sw]: phi^3 theory and the 1-loop integral --> real-valued vs imaginary part. Unitarity of the S-matrix and the optical theorem [P 7.3] [Sw 24.1]. Working this out explicitly for 1-loop contribution to propagator and verifying imaginary part arising from intermediate states going on-shell etc. Unitarity for tree-level amplitudes.
The Veneziano amplitude (open strings) and analyticity properties (or what is Not a quantum field theory!) [from Green,Schwarz,Witten, "Superstring Theory" vol.1, ch.1, beginning].
very brief glimpse at MSbar (minimal subtraction) [P 11.4]; broad recap of renormalization schemes; an overview of Wilsonian renormalization (Euclidean continuations and statistical physics, critical phenomena; physical UV cutoffs; integrating out thin momentum shells, low energy effective actions). [P ch.12]
Integrating out thin momentum shells in phi4 theory explicitly at 1-loop, and RG flows of couplings; running of the coupling towards lower energies, the beta-function; Wilson-Fisher fixed point. [P 12.1]
Renormalization conditions at running scales; the Callan-Symanzik equation and beta-functions; explicit evaluation for phi4 theory [P 12.2]; generalities on RG flow equations and beta-functions; a very cursory glimpse of QCD, asymptotic freedom and strong coupling IR. [P 12.2-12.5]
* midsem, endsem, assignments (or reading project)
Suggested follow-up reading:
U(1) gauge theory (Maxwell electromagnetism),
free field quantization (radiation gauge, Lorentz gauge, negative norm
states etc);
QED and elementary scattering processes
[P ch.4-7, Sw ch.8-9, 13];
Nonabelian gauge theories and the Standard Model [P part III, Sw part IV].