PHY 6648 "Quantum Field Theory I"
Class Diary for Fall 2014


Date Notes
Monday 8/25 Introductions, course policies. Inspirational reading (handout): F. Wilczek, "Quantum Field Theory", Rev. Mod. Phys. 71, S85 (1999), also available as hep-th/9803075. Alternative inspirational reading: Permanent Jobs Elusive for Recent Physics PhDs.
Wednesday 8/27 Calculations and simulations in high energy particle physics.
Friday 8/29 Overview of a particle physics experiment. Experimental efficiencies, detector acceptance. The principle of Monte Carlo integration.
Monday 9/1 Labor Day - no class.
Wednesday 9/3 Invitation (Chapter 1). (Overview of the big picture.)
Friday 9/5 Review of Lagrangian and Hamiltonian formulation of particle dynamics. Generalization to classical field theory. Derivation of the Euler-Lagrange equations. Hamiltonian field theory.
Monday 9/8 Example: Klein-Gordon action. Klein-Gordon equation. Hamiltonian description. Begin derivation of Noether's theorem.
Wednesday 9/10 Finish derivation of Noether's theorem. Energy-momentum tensor. Symmetries and conservation laws. Translations: energy and momentum. Higher derivative lagrangians. Ostrogradsky instability.
Friday 9/12 Internal U(1) symmetry, charge conservation. Rotations, angular momentum. Second quantization. Quantization conditions.
Monday 9/15 Review of QM of simple harmonic oscillator. Ladder operators and their commutation relations. Consistency check of the quantization conditions.
Wednesday 9/17 Derivation of the Hamiltonian in terms of the ladder operators. Eigenstates of the Hamiltonian and the momentum operator. Particle interpretation. Statistics.
Friday 9/19 Lorentz invariant measure (see homework). Normalization of states. Comparison of conventions. Heisenberg representation.
Monday 9/22 Causality.
Wednesday 9/24 Time ordered product. Feynman propagator. Derivation of the Feynman propagator for a scalar field.
Friday 9/26 First midetrm exam and solutions
Monday 9/29 Lorentz invariance of the Lagrangian and the field equations for the scalar and electromagnetic field. (Chapter 3.1).
Wednesday 10/1 Introduction to groups. Examples of finite (discrete) groups. Examples of continuous groups: O(2), SO(2), U(1), O(3) and SO(3). The importance of generators.
Friday 10/3 Algebra of the generators. The group SU(2). Representation of spatial rotations in terms of SU(2). The Lorentz group: generators of rotations and their algebra. The Lorentz group: generators of boosts and their algebra.
Monday 10/6 The SU(2)xSU(2) structure of the Lorentz group. Algebra of the A and B generators. (1/2,0) and (0,1/2) Weyl spinors and their transformation properties. Weyl equations.
Wednesday 10/8 Helicity. Building Lorentz-invariant objects out of Weyl spinors. Reality properties. Majorana spinors. The Dirac Lagrangian and its symmetries (see Problem 3 from HW Set No. 5).
Friday 10/10 Free-particle solutions of the Dirac equation. (Chapter 3.3) Dirac spinors and the Klein-Gordon equation. Plane-wave solutions. u and v spinors: general form. Normalization conditions for u and v spinors. Spin sums (end of Section 3.3).
Monday 10/13 Quantization of the Dirac field (Section 3.5).
Wednesday 10/15 The spin of a Dirac particle. Angular momentum from Noether's theorem. Angular momentum operator and its eigenvalues.
Friday 10/17 Homecoming - no class.
Monday 10/20 Interaction Lagrangians. Requirements. Dimensional analysis. Examples: phi-fourth, Yukawa, QED. Gauge invariance. Covariant derivatives.
Wednesday 10/22 Section 4.2: Perturbation expansion of correlation functions: Free scalar field in the Schrodinger and Heisenberg picture, interacting scalar field. Time evolution operator U(t,t0). The differential equation for U and its solution. Time-ordering and exponentiating the solution. Eq. (4.31).
Friday 10/24 Section 4.3: Wick's theorem. Normal ordering versus time ordering. Contractions. Simple Feynman diagrams. Feynman diagrams (section 4.4). 2-point correlation function including interactions. Combinatorics of the first-order term. Symmetry factors.
Monday 10/27 Feynman rules for phi-fourth theory. Example of a third-order term. Feynman rules in momentum space: momentum conservation at each vertex, factors at external points. Connected versus disconnected diagrams. Examples of factorizing the vacuum bubbles: a 2-point function, a 4-point function.
Wednesday 10/29 Cross-sections (section 4.5). Definitions. Formula for 2 to 2 scattering in the CM frame. S-matrix. T-matrix. The general formula for 2 to N scattering. Decay rates.
Friday 10/31 Second midterm exam.
Monday 11/3 2-body phase space. Cross-section formula for the case of equal masses. Section 4.6: Calculation of T-matrix elements in terms of Feynman diagrams. Examples of disconnected diagrams. Amputated diagrams. Contractions with external states. Example: the first order term in the 2 to 2 amplitude in phi-fourth theory.
Wednesday 11/5 2 to 2 cross-section in phi-fourth theory. Feynman rules for phi-fourth theory.
Friday 11/7 Feynman rules. Propagators for spin 0, 1/2, 1 and 2 particles. Vertices. External fermions. External photons. Minus sign rules for fermions. Elementary processes of QED. Begin calculation of the matrix element squared for electron-positron annihilation into muon pairs.
Monday 11/10 Finish the calculation of the cross-section for e+ e- into mu+ mu-. Spin sums and averaging. Trace technology of gamma matrices.
Wednesday 11/12 The differential cross-section in terms of the scattering angle. Mandelstam variables. Crossing symmetry.
Friday 11/14 Electron-muon scattering. Compton scattering. Spin sums for photons. Organising the calculation. Evaluation of traces. Crossing symmetry: e+ e- annihilation into photons. High energy limit.
Monday 11/17 Monte Carlo integration methods and their application in particle physics. Introduction to CalcHEP.
Wednesday 11/19 CalcHEP tutorial. See, for example, KC's TASI lecture.
Friday 11/21 CalcHEP quiz.
Monday 11/24 Review of the CalcHEP quiz.
Wednesday 11/26 Thanksgiving holiday - no class.
Friday 11/28 Thanksgiving holiday - no class.
Monday 12/1 Discussion of singularities in the s,t and u channels. Types of radiative corrections. Ultraviolet and infrared divergences.
Wednesday 12/3 Quantum computation of soft bremsstrahlung. Section 6.2: The electron vertex function: formal structure. Consequences from Lorentz and gauge invariance. Form factors. Electric charge and magnetic moment of the electron.
Friday 12/5 Third midterm exam.
Monday 12/8 Section 6.3: The electron vertex function: evaluation. Feynman parameters. Manipulation of the denominator. Evaluation of loop integrals. Pauli-Villars regularization. Finish the calculation of the electron vertex function. Section 6.4 The electron vertex function: IR cancellation.
Wednesday 12/10 Last lecture: distribute final exam. Overview of past homework problems.