Teaching Term and Class Location:Second Term (MSci) 10 January - 25 March 2011
Aims and Objectives:
Quantum Mechanics and Special Relativity (part revision): (~ 6 hours)
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
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.
Written examination of 2 1/2 hours contributing 90% and coursework contributing 10%
semester eight homework assignments will be given. The
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.
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",
(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.)