Introduction to the Renormalization group.

Pronob Mitter (1)

1 L2C - Laboratoire Charles Coulomb

In these lectures I will introduce and explore properties of the Renormalisation Group (RG) both in its discrete and continuous forms. Topics to be discussed include multi scale expansions, the RG, Gaussian fixed points, Wick products from the RG point of view, ultraviolet cutoff removal, flow equations and perturbative flows, trivial and non-trivial fixed points, and critical field theories. Rigorous Discrete RG analysis. I will discuss a rigorous application for a non-trivial fixed point.

Mots clés: Renormalization group; rigorous control for a non-gaussian fixed point; multi-scale expansions; Gaussian fixed points; discrete flows; continuous flows; ultraviolet cutoff removal; critical field theories

Domaines: Physique mathématique [math-ph]; Physique mathématique [math-ph]

Pronob Mitter. Introduction to the Renormalization group.. Scaling limits, rough paths, quantum field theory, Sep 2018, Cambridge, United Kingdom. ⟨hal-01935444v2⟩