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Gauge theories - NJSF137

Title:	Kalibrační teorie
Guaranteed by:	Institute of Particle and Nuclear Physics (32-UCJF)
Faculty:	Faculty of Mathematics and Physics
Actual:	from 2015
Semester:	summer
E-Credits:	5
Hours per week, examination:	summer s.:2/2, Ex [HT]
Capacity:	unlimited
Min. number of students:	unlimited
4EU+:	no
Virtual mobility / capacity:	no
State of the course:	taught
Language:	Czech
Teaching methods:	full-time
Teaching methods:	full-time

Guarantor:	Mgr. Tomáš Sýkora, Ph.D.
Incompatibility :	NJSF134, NJSF136

Annotation -

Last update: T_UCJF (18.04.2012)

for undergraduates who finished quantum mechanics and graduates

Course completion requirements -

Last update: Mgr. Tomáš Sýkora, Ph.D. (12.06.2019)

The exam is oral. The student gets one problem to solve and three questions from the topics mentioned in the lecture syllabus.

Literature -

Last update: T_UCJF (20.03.2015)

Ta-Pei Cheng, Ling-Fong Li, Gauge Theory of elementary particle physics, ISBN-13: 978-0198519614

Kerson Huang, Quarks, Leptons & Gauge Fields, ISBN-13: 978-9810206598

Mikio Nakahara, Geometry, Topology and Physics, ISBN-13: 978-0750306065

Requirements to the exam -

Last update: Mgr. Tomáš Sýkora, Ph.D. (12.06.2019)

The exam is oral. The student gets one problem to solve and three questions from the topics mentioned in the lecture syllabus.

Syllabus -

Last update: T_UCJF (18.04.2012)

gauge transformation, gauge group, spatial and inner symmetries, unitary symmetry, isospin, represenation of

(abelian) gauge theory - global and local gauge invariance, Bohm-Aharon effect and Dirac phase, spontaneous symmetry breaking, classical solutions with final energy, magnetic flux quantization, soliton solutions and vortices

(non-abelian) gauge theory - Li groups and algebras, global and local gauge invariance, topological properties, abelian and non-abelian monopols, Dirac string, symmetry breaking, soliton solutions

path integral - transition amplitude, time-ordering, Euclidian space-time, perturbation theory and loop expansion, grassmann variables

quantization of gauge fields - gauge fixing, Fadeev-Popov quantization, free electromagnetic and Yang-Mills fields, ghosts, θ-vacuums, instantons

renormalization - finite renormalization, renormalization in quantum field theory

renormalization group equation - renormalization group, Callan-Symanzik equation, anomalous dimension, non-perturbative renormalization