Electroweak Interactions

Relativistic quantum mechanics.
Klein-Gordon's equation. Plane wave solutions of Klein-Gordon's equation.
Negative energy solutions. Probability current. Negative probability.
Relativistic invariance of Klein-Gordon's equation.
Klein's paradox. Quantum mechanics and relativity.
Dirac's equation. Properties of alpha and beta matrices. Pauli-Dirac's representation.
Plane wave solutions of Dirac's equation. Spinors. Negative energy solutions.
Covariant form of Dirac's equation: gamma matrices.
Properties of gamma matrices.
Probability current. Spinor adjont e conserved probability current.
Normalization of spinors.
Negative energy solutions interpretation: Dirac sea model: holes.
Generators of four-vectors Lorentz transformations.
Generators of spinors Lorentz transformations.
Relativistic invariance of Dirac's equation.
Orbital angular momentum non conservation in Dirac's equation.
Intrinsic angular momentum (spin) non conservation.
Conservation of total angular momentum.
Spin relativistic description: helicity.
Spin relativistic description using particle's rest frame. Four vector polarization s.
Completeness relations for spinors.
Electromagnetic interaction trough minimal substitution.
Low energy limit of Dirac's equation.
Coulomb scattering of spin 0 particle. Cross section.
Coulomb scattering of spin ½ particle. Gamma matrices trace techniques.
Trace of gamma matrices products.
Scattering of polarized particles. Extension of gamma matrices trace techniques: spin projectors.
Gamma5 matrix.
Polarization effects in Coulomb scattering. Helicity conservation in the high energy limit.

Introduction to quantum field theory
Fourier analysis of the Klein-Gordon field
The classical electromagnetic field. Coulomb gauge. Electromagnetic waves.
Fourier analysis of the electromagnetic field. Field decomposition in oscillators.
Blackbody radiation. Classical model of blackbody radiation. Ultraviolet catastrophe.
Plank Hypothesis. Quantum distribution of blackbody radiation.
Introduction to quantum field theory.
Quantum harmonic oscillator. Algebraic solution. Creation and annihilation operators.
Number operator and Hamiltonian. Eigenstates of number and of Hamiltonian operators.
Quantization of a scalar real field. Occupation number Fock space.
States normalization. Symmetry of the states and commutation rules.
Number operators and Hamiltonian.
Field operators. Lagrangian for classical field.
Canonical quantization of the real Klein-Gordon field. Calculation of the Hamiltonian.
Noether's theorem. Space-Time invariances and energy-momentum tensor.
Complex Klein-Gordon scalar field. Quantization of the complex Klein-Gordon scalar field.
Global gauge invariance. Hamiltonian and charge operator. Particles and anti-particles.
Quantization of the Dirac field. Hamiltonian and commutation rules.
Global gauge invariance and conserved current. Particles and anti-particles.
Local gauge invariance and Quantum Electrodynamics (QED).
Gupta-Bleuler electromagnetic field quantization.
Interacting fields. Quantum oscillator with anharmonic term.
Scattering and S-matrix formalism. Perturbative expansion and Dyson series.
Observables: cross sections and decay widths.
Coulomb scattering in quantum field theory.
Electromagnetic interaction and fermions scattering. Photon propagator.
Feynman rules.
Two bodies final state kinematics. Two bodies final state phase space.
Photon propagator and gauge invariance.

Weak Interactions
Fermi's theory of neutron beta decay. Current-Current interaction.
Three bodies decay kinematics. Phase space for three bodies final state.
Non relativistic approximation. Nuclear spin variation.
Fermi's theory generalization.
Scalar, vector, axial vector, tensor and pseudo-scalar couplings.
Decay width calculation. Electron energy distribution. Experimental measurements.
Electron-neutrino angular correlations. Allen experiment.
Beta decay lifetime.
Lorentz group. Structure of the Lorentz group.
Spinors inversion. Lorentz transformation of bilinear covariants.
Parity violation. Theta-tau paradox. Dalitz plot. Experiments through a mirror.
Parity and charge symmetry violation in beta decay. CP invariance of beta decay.
Introduction of parity violating terms in the beta decay Hamiltonian.
Electron polarization in beta decay. Electron polarization measurement.
Bargman-Telegdi-Michel formula and electron spin rotation. Frauenfelder experiment.
Beta decay Hamiltonian. Chiral projections.
Chiral projections and zero mass particles.
Chiral projections and anti-particles. Left-handed chiral currents.
Universality of weak interaction. Mu lepton decay.
Weak hadronic current. Pi meson decay.
Electron polarization in pi meson decay
Tau lepton decay. Decay fraction for the pi meson neutrino final state.
Polarized tau lepton decay.
Tau lepton polarization measurement in positron electron collisions at LEP.
Hadrons weak decays.
Isotopic properties of hadronic current: isospin formalism.
Hadronic current matrix elements and weak form factors. Vector hadronic current.
Hadronic electromagnetic current and electromagnetic form factors.
Gordon's electromagnetic current decomposition.
Electromagnetic form factors of proton, neutron and pi meson.
Electromagnetic current and Isospin. Gell-Mann's CVC hypothesis.
CVC hypothesis test: weak beta decay of pi meson.
Weak decays with variation of strangeness.
Selection rules DeltaS = ±1 e DeltaS = DeltaQ.
Cabibbo's hypothesis. Cabibbo's angle.
Neutrino fermion interactions. Neutrino electron and anti-neutrino electron scattering.
Neutrinos quark scattering.
Fermi interaction difficulties and intermediate vector boson W (IVB).
W boson propagator.
Neutrino cross-sections in the IVB model. Difficulties of IVB model.
Divergence of the longitudinally polarized W boson pair cross section at high energies.
Neutrino- nucleon deep inelastic scattering.
Kinematic variables. x and y variables. Bjorken's scaling.
Nucleon parton model.
Neutrino nucleon cross-sections calculation in the parton model. Experimental measurements.
Quark distributions in nucleons measurement.

Electroweak interactions and Standard Model
Discovery of neutral currents. Neutral weak current interactions parametrization.
Vector and axial vector couplings.
Neutral current mediated neutrino quark cross sections.
Quarks vector and axial vector coupling constants measurement.
Neutrino electron scattering and lepton's coupling constants measurement.
Standard Model symmetries. Weak isospin and weak hypercharge.
The SU(2)_L x U(1)_Y group. Weak isospin and weak hypercharge currents.
Local gauge invariance and interaction vertices.
Spontaneous symmetry breaking. Charged currents. Neutral electromagnetic current. Weak neutral current.
Higgs model: complex scalar field, local gauge invariance and electromagnetic field.
Interaction terms and photon mass.
Higgs mechanism in the standard model. Higgs field and spontaneous symmetry breaking.
Masses of the vector bosons Z and W. Coupling constants.
Radiative corrections. Introduction to renormalization.
Electromagnetic propagator renormalization. Lamb's shift.