# Lattice Gauge Theory: course contents

## Section 1

### Path integral in quantum mechanics

Non-relativistic path integral problems, discretization, 0+1 dimensional field theory, solving by transfer matrix, doing numerical simulations. (Use Smit and Lepage)

### Connection between statistical mechanics and QFT

Example of free field theory mapping into random walk problem. Choice of scaling. Introduce fermions, Grassman variables. (Use Itzykson and Drouffe and my old notes)

### Lattice gauge theory basics: Z(2), U(1)

Lattice as a means of regulating infinities, numerical renormalization, introduce U(1) LGT. Introduce Z(2) LGT; gauge invariant variables, gauge fixing. (Use Kogut's review and Wilson)

## Section 2

### Metropolis Algorithm

Define Metropolis algorithm, necessity of detailed balance, extension to multi hit and heat-bath algorithm. (Use Lepage, Creutz)

### Reweighting

Basic reweighting, multi-histogram method. (Use Ferrenberg and Swendson, my notes)

### Statistical treatment of data

Statistical treatment of independent data (central limit theorem), breakdown of CLT and analysis of autocorrelations, applications to reweighting. (Use Numerical Recipes and Sokal)

## Section 3

### Finite temperature field theory

Introduction, dimensional analysis, Fourier transforms, bosons and fermions, pressure.

### Scaling and beta function

Renormalization generates scale, numerical renormalization, T_{c}/Λ_{MS}.

### Finite size scaling

Use of finite size scaling to obtain critical indices (Use Engels, old Bielefeld papers)

## Section 4

### Chemical potential

Global symmetries, conserved quantum numbers, chemical potential, sign problem. (Use Gavai, Karsch and Hasenfratz).

### Avoiding the sign problem

Expanding in Taylor series, diagrammatics, stochastic trace evaluation.

### Fermi liquids

Changing ensembles, finding quantum numbers.

Sourendu Gupta. Created on Oct 05, 2005.