Quantum Field Theory |
Quantum field theory is at the heart of modern physics and forms the backbone of the standard model, which is our current best understanding of the laws of particles and forces. The reputation of QFT is that it is very difficult to learn. The book assumes some familiarity with quantum mechanics and special relativity. |

The readership is graduate students in theoretical physics. This book is clearly of a pedagogical nature and contains very detailed worked examples and proofs of statements.

The book consists of 11 chapters.

Chapter 1 gives a general overview of particle physics. The reader is exposed to the basic idea of QFT here and the 4 forces of nature. This chapter gives one a taste for the standard model though the book is not really a book about particle physics.

Chapter 2 introduces single-particle relativistic wave equations. Here the Klein-Gordon equation the Dirac equation & antiparticles, the Maxwell and Proco equations are covered. The importance of the Lorentz and Poincare groups in physics are outlined. The differential geometry of Maxwell’s equations is also presented.

Classical field theory is the topic of Chapter 3. Here the Lagrangian formulation and variational principles are reviewed. The Bohm-Aharonov effect is presented as is Yang-Mills theory from a geometric perspective.

Chapter 4 deals with the canonical quantisation and particles. Due to technical difficulties the Klein-Gordon and Dirac equations cannot be single particle equations. In this chapter the reader starts to deal with quantum field theory as a theory of “many particles”. The real and complex Klein-Gordon fields, Dirac fields and the electromagnetic field are dealt with via canonical quantisation.

From a modern perspective path-integrals are the root to quantisation of fields. In Chapter 5 the Feynman path-integral formulation of quantum mechanics is presented. Topics covered here include perturbation theory & S-matrices and Coulomb scattering. This chapter lays down the ideas of path-integrals ready for QFT.

Chapter 6 develops the path-integral quantisation and Feynman rules for scalar and Dirac fields. Topics covered include: generating functionals, functional integration, Green’s functions & propagators, interacting fields, fermions & anticommuting variables and S matrix formula.

Chapter 7 moves on to discuss path-integral quantisation of gauge fields. Topics covered include: gauge fixing, Faddeev-Popov ghosts, Feynman rules in the Lorentz gauge, the Ward-Takahashi identity in QED, the BRST transformations and the Slavnov-Taylor identities.

Spontaneous symmetry breaking and the Weinberg-Salam model are the topic of Chapter 8. Topics covered include: the Goldstone theorem, spontaneous breaking of gauge symmetries, superconductivity and the Weinberg-Salam model.

Chapter 9 covers the subject of renormalisation. Topics covered include: divergences in QFT, dimensional analysis, regularisation, loop expansions, counter-terms, the renormalisation group, 1-loop renormalisation of QED, renormalisabilty of QCD, asymptotic freedom, anomalies, and renormalisation of Yang-Mills theories with spontaneous symmetry breaking.

Chapter 10 introduces the notion of topological objects in field theory. Topics covered include: the sine-Gordon kink, the Dirac monopole, instantons and theta-vacua.

N= 1 supersymmety in 4 dimensions is the topic of Chapter 11. The theory is built at first in component form and then the power of superspace methods are exposed. Topics covered include the super-Poincare algebra, superspace & super fields, chiral super fields and the Wess-Zumino model.

Paperback: 507 pages

Publisher: Cambridge University Press; 2 edition (6 Jun 1996)

Language English

ISBN-10: 0521478146

ISBN-13: 978-0521478144