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Durham University

Centre for Particle Theory

Renormalization Group

8 Lectures Dr V. Niarchos

The course introduces the concept of renormalisation group flow in quantum field theory building on previous lessons about renormalisation in other lectures on QFT. Applications to different field theories, including gauge theories, will be described.

Outline of the course

- Wilson's renormalization group. Brief review of regularisation/renormalization in continuum QFT with examples. Introduction of Wilson's renormalization group using the path integral formulation of QFT. Implementation in scalar $\phi^4$ theory.

- Callan-Symanzik equation. Renormalisation conditions. Callan-Symanzik equations. Introduction of $\beta$ and $\gamma$ functions. Renormalisation group equations.

- Renormalisation group flow in renormalised perturbation theory. Examples in scalar $\phi^4$ theory in different dimensions, QED, non-abelian gauge theories. Asymptotic freedom in gauge theories.

Books for the course

M. E. Peskin and D. V. Schroeder, An introduction to QFT, (Addison Wesley, 1994)
J. Zinn-Justin, Quantum field theory and critical phenomena, (Oxford University Press, 2002)
K. G. Wilson and J. B. Kogut, The Renormalization group and the epsilon expansion, Phys. Rept.12:75-200, 1974.