PP2: Relativistic Quantum Mechanics

Module title: Relativistic Quantum Mechanics (PP2)

Module convenor: Dr. Michal Kreps (Warwick)

Module aims:

To provide an introduction to calculating scattering amplitudes in high energy physics using perturbation theory. It is not a general introduction to relativistic quantum mechanics and is specialized and intended for high energy physics students only. It is not recommended for non high energy physics students.

Learning objectives:

Use of four-vectors and index notation in relativistic equations.
Understand problems of interpretation in single particle model of RQM.
Use of perturbation theory and interaction terms to arrive at a Transition Amplitude.
Understand the properties of the Dirac equation.
How to calculate physical quantities from a set of Feynman Rules.
Understand spin sums and trace techniques for calculations.

Syllabus

Lecture 1: Special Relativity and Lorentz Invariance
Lecture 2: Examples of Lorentz Invariance: Maxwell and Klein Gordon Equations
Lecture 3: Perturbation Theory for Particle Scattering
Lecture 4: Coulomb Scattering of Charged Spin-0 Particles
Lecture 5: Invariant Amplitudes, Feynman Diagrams and Cross-Sections
Lecture 6: Calculating Cross-Sections for Spin-0 Scattering
Lecture 7: The Dirac Equation
Lecture 8: Dirac Equation: Spin, Antiparticles and Feynman Rules
Lecture 9: Coulomb Scattering of Charged Spin-1/2 Particles
Lecture 10: Spin Sums and Trace Techniques

Assessment

Assessment will be based on returned solutions to problems. They will be set after each lecture with return deadline once a week (same day for all lectures in single week). Marks on the problems sheet is indicative and might be adjusted based on future problems. Problems are available in regularly updated file (Last update on 23. October).

Recommended Texts

There is no set text, and I recommend finding one (or better several!) that suit you best. The course material is mostly covered in the following three books:

  • Quarks and Leptons: An Introductory Course in Modern Particle Physics by F. Halzen and A. Martin
  • Gauge Theories in Particle Physics Volume 1 by I. Aitchison and A. Hey
  • Introduction to Elementary Particles by D. Griffiths

You may also find the following useful for breadth/depth and for later courses on quantum field theory.

  • Modern Quantum Mechanics by J. Sakurai
  • Advanced Quantum Mechanics by J. Sakurai
  • The Principles of Quantum Mechanics by P. Dirac
  • Quantum Mechanics Volumes 1 and 2 by C. Cohen-Tannoudji and B. Diu
  • Relativity : Special, General and Cosmological by W. Rindler
  • A first course in General Relativity by B. Schutz
  • Classical Electrodynamics by J. Jackson
  • Classical Electricity and Magnetism by W. Panofsky and M. Philips
  • Classical Mechanics by H. Goldstein, C. Poole and J. Safko
Duration: 
1h on Tue, 1h on Wed, 1h on Thu, 10h total (first week only Tue and Thu)
Academic year: 
2013-2014
Starts: 
08/10/2013 - 11:00