Regularization (physics)

Abstract: Algebraic preliminaries Euclidean path integrals in quantum mechanics Path integrals in quantum mechanics - generalizations stochastic differential equations - Langevin, Fokker-Planck equations functional integrals in field theory generating functionals of correlation functions - loopwise expansion divergences in pertubation theory, power counting regularization methods introduction to renormalization theory - renormalization group equations dimensional regularization and minimal subtraction - calculation of RG functions renormalization of composite operators - short distance expansion linearly realized symmetries and renormalization non linearly realized symmetries - the examples of the non linear sigma-model models on homogeneous spaces in two dimensions tensorial analysis on Riemannian manifolds symmetric spaces - non local conservation laws, renormalization group Slavnov-Taylor and BRS symmetry - stochastic field equations renormalization and stochastic field equations - supersymmtery Abelian gauge theories non-Abelian gauge theories the standard model - anomalies renormalization of gauge theories - general formalism critical phenomena - general considerations mean field theory for ferromagnetic systems general renormalization group analysis - the critical theory near dimension four scaling behaviour in the critical domain corrections to scaling behaviour calculation of universal quantities the (phi squared) squared field theory in the large N limit ferromagnetic order at low temperature - the non linear sigma-model a few two-dimensional models - bosonization technique the 0 (2) non linear sigma-model critical properties of gauge theories large momentum behaviour in field theory critical dynamics field theory in a finite geometry - finite size scaling instantons in quantum mechanics - the anharmonic oscillator quantum mechanics - generalization unstable vacua in field theory degenerate classical minima and instantons perturbation theory at large orders and instantons - the summation problem the "phi to the fourth" field theory in dimension four fermions and large order behaviour multi-instantons in quantum mechanics

Abstract: Preface 1. From particle to fields 2. Second quantization 3. Feynman path integral 4. Functional field integral 5. Perturbation theory 6. Broken symmetry and collective phenomena 7. Response functions 8. The renormalization group 9. Topology 10. Nonequilibrium (classical) 11. Nonequilibrium (quantum) Index.