Theoretical Particle Physics

About this course:

Exercise 1:

Keywords: Lorentz Transformation, Covariant Four-vector, Lorentz Invariant, Chain Rule, Dirac Matrices, Dirac Representation, Pauli Matrices, Dirac Equation, Plane Wave Solutions, Dirac Spinor, Conjugate Spinor, Hermitian Conjugate, Adjoint Dirac Equation, Dirac Probability Current, Conserved Current, Charge Conjugation Operator

Exercise 2:

Keywords: Lorentz Transformation, Lorentz Invariants, Three-volume Element, Four-volume Element, Delta Distribution, Phase Space Element, Lagrangian Density, Noether’s Theorem, Complex Scalar Fields, Euler-Lagrange Equation, Equation of Motion, Symmetry of the Lagrangian, Noether Current, Classical Electromagnetic Field Equations, Action, Maxwell’s Equations, Dynamical Variables, Energy-momentum Tensor, Divergenceless

Exercise 3:

Keywords: Two-body Scattering, Mandelstam Variables, Lorentz Invariants, Center of Mass Energy, Fixed-target Scattering, Center of Mass Frame, Differential Cross Section, Reduced Amplitude, Laboratory Frame, Incident Flux Factor, Phase Space Integrals, Unit Solid Angle, Cylindrical Symmetry, Gamma Matrices, Properties

Exercise 4:

Keywords: Chiral Basis, Charge Conjugation, Parity, Time Reversal, Dirac Field, Transformation Properties, Free Dirac Equation, Free Dirac Lagrangian, Probability Current, Charge Density, Charge three-current, Spin Sums, Dirac Scalar, Dirac Matrix, Yukawa Theory, Scattering of Fermions, Feynman Diagrams, Matrix Element, Feynman Rules, Spin-averaged Matrix Element, Differential Cross Section, Center of Mass Frame

Exercise 5:

Keywords: Transition Amplitudes, Second Order Perturbation Theory, Iterated First Order, External Fields, Internal Field, ϕ³ Theory, Schrödinger Picture, Wave Functions, Lorentz Symmetry, On-shell Particles, Scattering Process, t-channel, Non-covariant Formulation, Old-fashioned Perturbation Theory, OFPT, Phase Space Integral, Mandelstam Variable, Quantum Electrodynamics, QED Lagrangian, U(1) Gauge Transformation, Noether Current, Equation of Motion, Fermion Fields, Conserved Current

Exercise 6:

Keywords: Quantum Electrodynamics, QED Lagrangian, Gauge-fixing Term, Lorentz Gauge, Equation of Motion, Photon Propagator, Feynman Gauge, Lorentz Gauge Condition, Scattering Processes, t-channel, s-channel, Current Conservation, Free complex Scalar Field, Scalar QED, Global Transformation, Noether Current, Probability Current, Klein-Gordon Theory, Local Transformations, Gauge covariant Derivative, Feynman Rules, Interactions, Vertex Factors, Polarization Vectors

Exercise 7:

Keywords: Proton Charge Radius, Electric Form Factor, Non-relativistic Limit, Charge Distribution, Spherical Coordinates, Spherically Symmetric, Point Interaction Term, Feynman Parameters, Loop Diagrams, Integrals

Exercise 8:

Keywords: Radiative Corrections, Loop Integrals, Minkowski Space, Euclidean Space, Wick Rotation, Vertex Correction, Quantum Electrodynamics, QED, Magnetic Moment of the Electron, Magnetic Moment of the Muon, Gordon Decomposition, Dipole Moment, Static Photons, g-2

Exercise 9:

Keywords: Vacuum Polarization, Correction to the Photon Propagator, Loop Integral, Wick Rotation, Regularization, Dimensional Regularization, Gamma Function, Effective Electric Charge, Jacobi Identity, Lie Algebra, Generators, Structure Constants, Adjoint Representation

Exercise 10:

Keywords: Free Dirac Field Lagrangian, Dirac Field, SU(N) Transformations, Gauge Symmetry, Gauge covariant Derivative, Minimal Coupling, Gauge Field, Gauge Invariance, Field Strength Tensor, Self couplings of the Gauge Bosons, Lie Algebra, Generators, SU(2), Pauli Matrices, Baryon Wave Function, SU(3) Gauge Transformation, Meson Wave Function, Infinitesimal SU(3) Transformation

Exercise 11:

Keywords: Standard Basis, Generators, SU(3), Fundamental Representation, SU(2) Algebra, Orthogonality Condition, Quadratic Casimir Operator, Quantum Chromodynamics, QCD, Up Quark, Down Quark, Color Indices, Color Structure, Matrix Element, Color Factor, Virtual Gluon, Squared Amplitude, External Quarks

Exercise 12:

Keywords: Muon Decay, V-A Interaction, W Boson Exchange, Muon-neutrino, Electron-Anti-neutrino, Electron, Feynman Diagram, Amplitude, Spin-averaged Amplitude, Dirac Conjugate, Three-body Phase Space, Rest Frame, Decay Rate, Lifetime

Exercise 13:

Keywords: Tree-level Process, Intermediate Vector Boson, Massive Spin-1 Boson, W Boson, Feynman Diagram, Transition Amplitude, Spinors, Polarization Vectors, Unitarity Violation, Longitudinal Helicity, Gauge Boson, Unitarity Bound, Complex Scalar Higgs Field, U(1) Charge, Potential, Vacuum Expectation Value, Mass Matrix, Real Fields, Complex Field, Eigenvalues, Eigenstates, Physical Masses, Physical States, U(1) Invariance, Mixing Angle, Goldstone’s Theorem

Exercise 14:

Keywords: Global U(1) Symmetry, Gauge Symmetry, Local U(1) Symmetry, Gauge Boson, Higgs Field, U(1) Charge, Vacuum Expectation Value, Higgs Mechanism, Higgs Boson, Unitary Gauge, Eigenstates, Mass Matrix, Higgs Doublet, SU(2) Gauge Transformation, Pauli Matrices, SU(2), Physical Particles, Left-handed Lepton Doublet, Right-handed Leptons, Weak Interactions, Non-abelian Field Strength Tensor, Lagrangian