# PP2: Relativistic Quantum Mechanics

Posted September 30th, 2015 by mpags

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.

## Module title: Relativistic Quantum Mechanics (PP2)

### Module convenor: Dr. Thomas Blake (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 assessment_6.pdf file.

### 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*

Academic year:

2015-2016Starts:

07/10/2015 - 11:00