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Centre for Particle Theory

Non-Perturbative Physics

16 Lectures Prof. P. Dorey

Many interesting phenomena in quantum field theory are non-perturbative i.e. can not be understood using perturbation theory. Solitons and instantons are topologically non-trivial solutions of classical field theories which are non-perturbative in nature. This course will discuss the classification, construction and properties of various types of solitons and instantons in a range of theories.

Outline of the course

Basics: Topology, Derrick's theorem, Bogomolny bounds, examples of solitons eg. kinks, vortices, lumps, Skyrmions.
Monopoles: Dirac monopoles, charge quantization, non-abelian monopoles, spontaneous symmetry breaking, BPS monopoles, moduli space metrics.
Instantons: Chern number, Self-dual Yang-Mills, 't Hooft ansatz, ADHM construction (if time).

Books for the course

N.S. Manton and P.M. Sutcliffe, Topological solitons (CUP, 2004)
R. Rajaraman, Solitons and instantons, An introduction to solitons and instantons in quantum field theory (North-Holland, 1982)
S. Coleman, Aspects of Symmetry (CUP, 1985)
Y. Shnir, Magnetic monopoles (Springer, 2005)