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Instructors: Dr. Dalibor Djukanovic
Event type:
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:
The course will assume familiarity with statistical mechancics, quantum mechanics, classical electrodynamics and special relativity.
Basic knowledge of nuclear and particle physics I, and quantum field theory I is useful.
Contents:
In this lecture we will cover the foundations and methods of lattice filed theory.
We will introduce the method of discretization as a means to solve a multitude of problems, starting with simple partial differential equations, to the formualation of classical and quantum mechanical system in a discretized setting. Our goal will be to understand the discretization of gauge theoreis on a lattice, where we will learn more about specific topics in Quantum Chromodynamics.
We will use Python (and Mathematica) as a programming language to implement some of the methods.
Contents:
- Statistical Mechanics and Quantum Field Theory
- Discretization of classical field theories
- Path integrals in quantum mechanics
- Euclidean correlation functions
- Discrete Models:
- Ising model
- Mean-field approximation
- Critical Exponents
- Transfermatrix
- Gauge Theories:
- Z2-Gauge theories
- Continuous gauge groups
- Haar measure
- Wilson loop
- Lattice QCD:
- Yang Mills actions
- Fermions on the lattice
- Gauge invariance in QED and QCD
- Static potential
- Hadronic matrix elements
- (Renormalization group and continuum limit)
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:
Lecture is organized in LMS.
If the lecture cannot be given in person, we will refrain to online courses using Big Blue Button.
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