Quantum Field Theory Problem Sets

These are Quantum Field Theory (I) problem sets (in French) that were the backbone of the exercise sessions that I gave in the years 2004/5-2009, complementary to the course taught by Costas Bachas and Adel Bilal. They are based on many standard textbooks, and notes by Boris Pioline. I hope they may be of use to you.

Bibliography, further references, and links on quantum field theory.

Problem sets (in French):

i) Conserved charges, Noether's method, global symmetries, local symmetries, gauge invariance, energy-momentum tensor. (08)

Problem set (postscript, .ps)

Problem set (portable document format, .pdf)

ii) The quantization of a complex scalar field. (08)

Problem set (postscript, .ps)

Problem set (portable document format, .pdf)

iii) The Casimir effect, the energy of vacuum fluctuations, the Casimir force. (08)

Problem set (postscript, .ps)

Problem set (portable document format, .pdf)

iv) The quantization and guises of the massive vector boson. (08)

Problem set (postscript, .ps)

Problem set (portable document format, .pdf)

v) An introduction to supersymmetric quantum mechanics. (08)

Problem set (postscript, .ps)

Problem set (portable document format, .pdf)

vi-vii) Supersymmetry, a few simple quantum field theories with supersymmetry, supersymmetry breaking. (08)

Problem set (postscript, .ps)

Problem set (portable document format, .pdf)

vii-viii) The creation of electron-positron pairs by a constant electric field. (08)

Problem set (postscript, .ps)

Problem set (portable document format, .pdf)

ix) A very brief introduction to solitons (and instantons). (08)

Problem set (postscript, .ps)

Problem set (portable document format, .pdf)

x) QED scattering amplitudes, lepton scattering, crossing symmetry and interaction channels. (08)

Problem set (postscript, .ps)

Problem set (portable document format, .pdf)

xi) A chiral anomaly (in two dimensions). (08)

Problem set (postscript, .ps)

Problem set (portable document format, .pdf)

xii-xiii) One-loop beta-function in non-abelian gauge theory, asymptotic freedom, QCD. (Based on Peskin-Schroeder and Weinberg.) (05)

xii-xiii) An effective field theory approach to superconductors (based on Polchinski, Abrikosov and various lecture notes available on-line). (06)

xii-xiii) Calculation of the abelian chiral anomaly following Fujikawa (based on Fujikawa's papers and Weinberg), and applications of anomalies to QCD with two flavours and neutral pion decay (following Peskin-Schroeder) as well as to anomaly cancellation in the gauge interactions of the Standard Model (following Weinberg). (07, 08)

Extra: A few very small exercises on Grassmann variables. (06)

Problem set Grassmann (postscript, .ps)

Problem set Grassmann (portable document format, .pdf)