Please take this page in conjunction with the Part III Guide to Courses Particle Physics, Quantum Fields and Strings section.

Please read in particular Introduction and prerequisites given in the Guide to Courses.

**Prerequisite areas**

The courses in high energy physics will require knowledge of the following subjects:

- Quantum Mechanics
- Special Relativity
- Classical Dynamics
- Statistical Mechanics (for the Statistical Field Theory course)
- You will also need mathematical fluency with suffix notation, vector calculus, Fourier transforms and the basics of complex functions, such as the residue theorem.

A brief description of the material you will need from Quantum Mechanics, Special Relativity and Classical Dynamics can be found in these notes. More details, together with Cambridge lecture notes which cover this material, are provided below.

## Quantum Mechanics

Quantum mechanics is needed for all courses in High Energy Physics. It is also needed for the courses in Cosmology. This material was covered in the undergraduate Cambridge mathematical tripos in "Quantum Mechanics" in Part IB and "Principles of Quantum Mechanics" in Part II.

### Reality check

You will need material from both basic and advanced undergraduate courses in quantum mechanics. You should be familiar with the concept of Hilbert spaces and states, observables as operators and Dirac bra-ket notation. You should also be happy with the harmonic oscillator and its description using ladder operators (sometimes called annihilation and creation operators), with the addition of angular momentum, and with perturbation theory.

You can use these workshop notes, prepared by Kai Roehrig, to help you get started. These notes include exercises to check your present level and to guide your study.

### Useful books and resources

- Quantum Mechanics by Prof. David Tong. This is an introductory course on quantum mechanics, based around wavefunctions and the Schrodinger equation.
- Principles of Quantum Mechanics by Dr David Skinner. This is a second course, covering Hilbert spaces, operators, the algebraic approach to the harmonic oscillator, angular momentum, and perturbation theory.

## Special Relativity

Special Relativity is needed for all courses in High Energy Physics (apart from Statistical Field Theory). It is also needed for all courses in Gravitational Physics and Cosmology. This material was covered in the undergraduate Cambridge mathematics tripos in "Dynamics and Relativity" in Part IA.

### Reality check

You should be familiar with Lorentz transformations, Minkowski space, 4-vectors, and the notation in which indices up and indices down differ by some minus signs.

You can check if you are at the required level by doing the Special Relativity exercise sheet prepared by Markus Kunesch.

### Prerequisites

It will be useful, but not essential, to be familiar with the Maxwell equations in 4-vector notation (i.e. using the electromagnetic tensor *F _{μν}*).

### Useful books and resources

- Dynamics and Relativity by David Tong. Chapter 8 covers special relativity.
- Electromagnetism by David Tong. Chapter 5 covers the Maxwell equations in relativistic form.

## Classical Dynamics

Both the Lagrangian and Hamiltonian approaches to classical mechanics are needed for nearly all the High Energy Physics courses. (Exceptions are the course on Statistical Field Theory and the course on Symmetries, Fields and Particles.) You will also need to know about the Lagrangian approach for the courses on General Relativity and Black Holes. This material is covered in the undergraduate Cambridge mathematics tripos in "Classical Dynamics" in Part II.

### Reality check

You should be happy with the variational approach to classical dynamics using the action, as well as its connection to the Hamiltonian approach.

### Useful books and resources

- Dynamics and Relativity by David Tong. This covers the simpler Newtonian approach to classical mechanics.
- Classical Dynamics by David Tong. This covers the Lagrangian and Hamiltonian approaches to classical mechanics.

## Statistical Mechanics

Statistical Mechanics is only necessary for the courses on Statistical Field Theory and Cosmology. It is also useful background, albeit not essential, for the course on Advanced Quantum Field Theory.

### Reality check

You should be happy with the basic ideas of partition functions and how they encode the thermodynamic properties of a system.

### Useful books and resources

- Statistical Physics by David Tong. This is an introduction to Statistical Mechanics and Thermodynamics. The last chapter on phase transitions is not a prerequisite, but has some overlap with the Statistical Field Theory course.