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Instructors: Dr. Dalibor Djukanovic
Event type:
online: Lecture/practice class
Displayed in timetable as:
08.128.746
Hours per week:
4
Credits:
6,0
Language of instruction:
Englisch
Min. | Max. participants:
- | -
Requirements / organisational issues:
Required: Statistical and Quantum Mechanics, Classical Electrodynamics and Special Relativity, Nuclear and Particle Physics 1.
Contents:
This course introduces principles and methods of lattice gauge theories.
First we will present strategies for the solution of partial differential equations via discretization. The consequences of the discretized setting in terms of the formulation of different theories, classical and quantum mechanical, will be discussed. For a realistic model we will explain methods and principles in detail. Finally we introduce gauge theories on the lattice, focussing on applications in QCD.
We will use Python and Mathematica as programming languages in this course.
Contents:
- Statistical Mechanics and Quantum Field Theory:
- discretization of classical field theories
- path integrals in Quantum Mechanics
- euclidean correlator functions
- Discrete models:
- Ising model
- Mean-field approximation
- critical exponents
- transfer matrix.
- Gauge theories:
- Z2 lattice gauge theorry
- continuous gauge groups
- Haar measure
- Wilson loop
- Lattice QCD:
- action
- fermions on the lattice
- gauge invariance in QED and QCD
- static potential
- renormalization group and continuum limit
- computing hadron properties
Recommended reading list:
G. Parisi, Statistical Field Theory (Frontiers in Physics, 66), Addison-Wesley, Redwood City 1988.
J.B. Kogut, An Introduction to Lattice Gauge Theory and Spin Systems, Rev. Mod. Phys. 51 (1979) 659.
C. Gattringer and C.B. Lang, Quantum Chromodynamics on the Lattice (Lect. Notes Phys. 788), Springer, Berlin Heidelberg 2010.
J. Smit, Introduction to Quantum Fields on a Lattice: a robust mate (Cambridge Lect. Notes Phys. 15), Cambridge University Press 2002.
H. J. Rothe, Lattice gauge theories: An Introduction, World Sci. Lect. Notes Phys. 74 (2005) 1–605.
I. Montvay and G. Münster, Quantum fields on a lattice, Cambridge, UK: Univ. Pr. (1994) 491 p. (Cambridge monographs on mathematical physics).
C. Morningstar, The Monte Carlo method in quantum field theory, hep-lat/0702020.
Digital teaching:
Organization (notes, etc.) via LMS
If an in-person lecture is not possible the lecture will be given over Big Blue Button.
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