Renormalization

Year
1

Academic year
2014-2015

Code
03001421

Subject Area
Mathematics

Language of Instruction
English

Mode of Delivery
Face-to-face

Duration
SEMESTRIAL

ECTS Credits
9.0

Type
Elective

Level
3rd Cycle Studies

Recommended Prerequisites

Basic knowledge of Dynamical Systems, Analysis and Statistics.

Teaching Methods

Lectures and tutorials: The contents of the syllabus are presented in the lectures, where examples are given to illustrate the concepts. There are also tutorials, where exercises and related problems are solved.

Learning Outcomes

The students will be provided with the basic tools for studying universal physical and dynamical laws.

Work Placement(s)

Syllabus

Feigenbaum universality and renormalization. Percolation models. X,Y model and BHP universality. Master equation. Pair approximation. Phase transitions. Path integrals. Feynman diagrams. Renormalization group. Scaling laws. Brownian motion. Levy processes. Monte Carlo simulation. Stochastic Loewner evolution. Conformal invariance.

Assessment Methods

Assessment
Exam: 100.0%

Bibliography

L. P. Kadanoff, Statistical physics: statics, dynamics and renormalization, World Scientific, 2000

A. Lesne, Renormalization methods: critical phenomena, chaos, fractal structures, John Wiley, 1998

W. D. McComb, Renormalization methods: a guide for beginners, Clarendon Press, Oxford, 2004

J. Zinn-Justin, Phase transitions and renormalization group, Oxford University Press, 2007