Relativistic Waves & Quantum Fields

MSci 4242/QMUL PHY-415 (Winter 2011)

This course is taught as part of the University of London Intercollegiate Physics MSci programme.

Teaching Term and Class Location:

Second Term (MSci) 10 January - 25 March 2011
Lectures will be held at University College in room UCL Physics A1 on Fridays from 10am - 1pm:
First lecture: 14 January // Final lecture: 25 March
If you do not know how to get to the classroom consult the Intercollegiate Physics MSci webpage.

Aims and Objectives:


This course provides a first introduction into the unification of last century's groundshaking revolutions in physics: Special Relativity and Quantum Mechanics. Relativistic wave equations for particles of various spins are derived and studied, and the physical interpretations of their solutions are analyzed. Students will learn about the fundamental concepts of quantum field theory, starting with classical field theory, quantisation of the free Klein-Gordon and Dirac field and the derivation of the Feynman propagator. Then interactions are introduced and a systematic procedure to calculate scattering amplitudes using Feynman diagrams is derived. Finally, the quantisation of the electro-magnetic field is discussed and the relativistic cross sections for various physically relevant examples are calculated.


Quantum Mechanics and Special Relativity (part revision): (~ 6 hours)

Schroedinger equation, wavefunctions, operators/observables, symmetries and conservation laws in QM; short introduction to Special Relativity: 4-vector notation, Lorentz transformations (LT), Lorentz invariance/covariance, LT of the electromagnetic field

Relativistic Wave equations: (~ 9 hours)

Klein-Gordon equation and probability density; Dirac equation, covariance and probability density, non-relativistic limit, spin, Feynman notation, plane wave solutions, Lorentz transformations of plane wave solutions; hole theory and anti-particles, vacuum polarisation; discrete symmetries: C & P & T symmetry and their relevance for electromagnetic and weak interactions, Dirac covariants; wave equations for massless fermions, neutrinos; Feynman interpretation of the Klein-Gordon equation; Dirac equation in an electromagnetic field, magnetic moment of electron, relativistic spectrum of Hydrogen atom.

Quantum Field Theory
: (~ 18 hours)

Classical field theory, Noether theorem, stress-energy tensor, symmetries and conserved currents; canonical quantisation of the Klein-Gordon field, creation and annihilation operators, vacuum energy, Casimir effect; quantisation of Dirac fermions, spin-statistics connection; commutators and time ordered products, the Feynman propagator; Dyson expansion; S-matrix, scattering amplitudes, transition rates; cross sections; Phi^4 theory scattering amplitude; decay rates of unstable particles; Wick's theorem and its application to perturbation theory, Feynman rules; quantisation of the electromagnetic field and Gupta-Bleuler formalism; interaction with the electron; Feynman rules & calculation of various scattering processes: Compton, electron-electron, electron-positron; spin sums & cross sections.

Lecture Notes:

Lecture notes: for the first half of the course here, and for the second half Part I, Part II.

The lecture notes of my previous course, Relativistic Quantum Mechanics (RQM), have some overlap with the material covered in RWQF and can be found here pdf .


Written examination of 2 1/2 hours contributing 90% and coursework contributing 10%


During the semester eight homework assignments will be given. The homeworks will be posted on the webpage every Friday and are due two weeks later (I collect them in the Friday lecture).
Late assignments will be marked to zero, unless you have medical or other valid reasons.

Assignment 1: pdf (issued 14/1/2011, hand in by 28/1/2011) solution

Assignment 2: pdf (issued 21/1/2011, hand in by 4/2/2011) solution

Assignment 3: pdf (issued 28/1/2011, hand in by 11/2/2011) solution

Assignment 4: pdf (issued 4/2/2011, hand in by 18/2/2011) solution

Assignment 5: pdf (issued 11/2/2011, hand in by 25/2/2011) solution

Assignment 6: pdf (issued 18/2/2011, hand in by 4/3/2011) solution part 1 2 3 4 5

Assignment 7: pdf (issued 25/2/2011, hand in by 11/3/2011) solution

Assignment 8: pdf (issued 4/3/2011, hand in by 25/3/2011) solution part 1 2 3

Office Hours: by appointment (email:

My office is in Physics 214 at QMUL.


Past exam papers: 2007, 2008, 2009, 2010

The exam paper will be accompanied by the following formula sheet.

Recommended Books:

A list of good books relevant for the course:

I.J. Aitchison & A.J. Hey, "Gauge theories in particle physics: Volume 1: From Relativistic Quantum Mechanics to QED", 3rd Edition, Taylor & Francis Adam Hilger. (a good introductory book, contains nice discussion of gauge invariance)

J. Bjorken and S. Drell, "Relativistic quantum mechanics" and "Relativistic quantum fields", McGraw-Hill. (an old but reliable source, in particular the first book is relevant to the first part of my course)

L.H. Ryder, "Quantum Field Theory", Cambridge University Press. (A nice and very pedagocical book, Chapters 1-6 are relevant for our course.)

M.E. Peskin and D.V. Schroeder, "An Introduction to Quantum Field Theory", Addison-Wesley.
(Very good book, which covers much more material than the course. This is THE book you should buy, if you have money for only one book on the subject and you are more serious about theoretical particle physics and/or phenomenology.)

S. Weinberg, "The Quantum Theory of Fields" in 3 Volumes., Cambridge University Press. (Advanced book on Quantum Field Theory from a Nobel laureate. Probably overwhelming for a first QFT book. The first chapters of the first volume are relevant for the course.)

C. Itzykson and J.-B. Zuber, "Quantum Field Theory", (Another classic but less pedagogical than Peskin-Schroeder; in particular Sections 1, 2 & 3 have a lot of overlap with the course.)  

F. Mandl, "Quantum mechanics", J Wiley.

W. Greiner, "Relativistic Quantum Mechanics: Wave Equations", Springer-Verlag. (Contains many examples and exercises worked through explicitly.)

  last updated 28/2/2011