This is an archive of the Quantum Field Theory II course. A pdf version of the outline is QFT 2 summary

**Extension section**

Here we cover some of the important topics that were not covered in the first semester. These include several functional methods and also techniques with fermions.

**Extension 1** – Notes and Extension 1 video – Very quick review, vacuum polarization via Feynman rules, quick review of Path Integral formulas, vacuum polarization via functional techniques, functional differentiation again.

**Extension 2 **– Notes and Extension 2 video – Perturbation theory via functional derivation, completing the vacuum polarization example, the determinant of a differential operator det (D2 +m2 ), det = exp tr ln identity, integrating out the scalar field, renormalization and effective Lagrangian.

**Extension 3** – Notes and Extension 3 video – Heat kernel method, Fermion path integral, Functional differentiation with anticommuting sources, Grassmann numbers, Spin statistics theorem, Dirac algebra, ordering in Feynman diagrams, gauge invariance example.

**Extension 4 ** – Notes and Extension 4 video – Chiral fermions, left and right fields, Majorana mass, spin sums for fermions and photon, traces of gamma matrices.

**Extension 5** – Notes and Extension 5 video – Practical group theory, SU(2) and SU(N), representations and transformation rules, constructing invariants, extracting predictions

** Gauge Theory section**

In this section we extend the treatment of gauge symmetry to nonabelian groups, explore some gauge theory features and give a full quantization of Yang-Mills gauge theories

**Gauge theory 1 ** – Gauge Theory 1 notes and Gauge theory 1 video – Nonableian gauge symmetry, the Yang Mills lagrangian, path integral quantization, problem with propagator, simple example of factoring out symmetry, constraining the path integral.

**Gauge theory 2** – Gauge theory 2 notes and Gauge theory 2 video – Review of path integral quantization, QED example, covariant gauges, Fadeev-Popov trick, ghosts, Yang Mills example, Feynman rules for Yang Mills.

**Gauge theory 3 **– Gauge theory 3 notes and Gauge theory 3 video – running coupling in QED, 1/epsilon determines logs, charge renormalization in Yang Mills, vacuum polarization, oddities of dimensional

regularization, calculating casimirs.

**Gauge theory 4** – Gauge theory 4 notes and Gauge theory 4 video – ghost and fermion contributions to running coupling, the overall beta function, matching across mass thresholds, scheme dependence, higher orders.

**Gauge theory 5** – gauge theory 5 notes and Gauge theory 5 video – g=2 from Dirac equation, calculating g-2 and the vertex correction.

** Effective Field Theory Section**

I treat the idea of effective field theory both in general and by use of the specific case of the linear sigma model.

**Effective field theory 1** – EFT 1 notes and Effective Field Theory 1 video – What is effective field theory, locality, QED effective Lagrangian, the energy expansion, linear sigma model, a low energy calculation and its effective Lagrangian

**Effective field theory 2 ** – EFT 2 notes and EFT 2 video – the exponential representation, recalculating the scattering amplitude, path integral connection, integrating out at tree level, start of matching.

**Effective field theory 3** – EFT 3 notes and EFT 3 video – Integrating out scalar, heat kernel, general form of effective L, which parameters to use, matching the effective theory and the full theory.

**Effective field theory 4 ** – EFT 4 notes and EFT 4 video – Power counting, Weinberg theorem, measuring vs matching, Rules of EFT, relevance of sigma model, explicit symmetry breaking, Wilson and EFT.

**Effective field theory 5 ** – EFT 5 notes and EFT 5 video – The operator product expansion, weak interaction example, the background field method, φ4 example, heat kernel, perturbative expansion, background field renormalization of the sigma model.

** Anomalies Section**

I treat symmetries and anomalies using primarily a path integral approach

**Anomalies 1** – Anomalies 1 notes and Anomalies 1 video – currents and path integrals, path integrals and symmetries, scale invariance in the Standard Model, The trace anomaly, calculating the path integral jacobian

**Anomalies 2 ** – Anomalies 2 notes and Anomalies 2 video – obtaining the trace relation, Feynman diagram approach, interpreting the trace anomaly, the simplest derivation via running charge, axial U(1) problem, starting the chiral anomaly calculation.

**Anomalies 3** – Anomalies 3 notes and Anomalies 3 video – shift of integration variable, the pi to 2 gamma story, anomalies and gauge currents

** Standard Model Section**

This is a very brief tour through the structure of the Standard Model

**Standard Model 1** Standard Model 1 notes and Standard model 1 video – quantum numbers, U(1) ambiguity, anomaly conditions, hypercharge assignments

**Standard Model 2** – Standard Model 2 notes and Standard model 2 video – Adding the Higgs, Gauge boson masses, Gauge currents for fermions, Math: doublet = anti-doublet, Yukawa couplings

**Standard Model 3** – Standard Model 3 notes and Standard model 3 video – Diagonalizing mass matrices, Neutrino masses and see saw mechanism, diagonalizing neutrino masses, VCKM and VPMNS , tree level weak decays.

**Standard Model 4 ** – Standard Model 4 notes and Standard model 4 video – the pion/kaon story, external sources method, enhanced symmetry, the effective Lagrangian, quark masses

**Standard Model 5 ** – Standard model 5 notes and Standard model 5 video – rare weak decays, inputs into W,Z physics, STU and precision tests, arguments for new physics beyond the Standard Model

** Supersymmetry Section**

These are two lectures which give a superficial overview of the structure of supersymmetric theories and the MSSM

**Supersymmetry 1** – Supersymmetry 1 notes and Supersymmetry 1 video – Weyl spinors, Wess-Zumino model, SUSY charges, SUSY algebra, auxiliary fields, superspace, chiral superfield, vector superfield, superpotential, F-terms and D-terms, SUSY model building

**Supersymmetry 2** – Supersymmetry 2 notes and Supersymmetry 2 video – properties of SUSY, the case for weak scale SUSY, construction of the MSSM, R parity, supersymmetry breaking, hidden sector, soft SUSy breaking, the Higgs sector,, EWSB, the mu problem, flavor issues.

** Gravity as a Gauge Theory Section**

These two lectures develop general relativity in a manner similar to our treatment of gauge theories. This emphasizes the field theoretic nature of general relativity.

**Gravity 1** – Gravity 1 notes and Gravity 1 video – Gauging Lorentz transformations, Spin transformation for fermions, local Lorentz invariance, vierbein, fermions and the spin connection, covariant derivative, forming the curvature, Einstein action and equations

**Gravity 2 ** – Gravity 2 notes and Gravity 2 video – review of gauge theory construction, exploring the action, higher invariants of the curvature, quantization and Feynman rules, background field renormalization, gravity as an effective field theory