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Theory of Gauge Fields - NTMF022

Title:	Teorie kalibračních polí
Guaranteed by:	Institute of Theoretical Physics (32-UTF)
Faculty:	Faculty of Mathematics and Physics
Actual:	from 2020
Semester:	winter
E-Credits:	4
Hours per week, examination:	winter s.:3/0, Ex [HT]
Capacity:	unlimited
Min. number of students:	unlimited
4EU+:	no
Virtual mobility / capacity:	no
State of the course:	taught
Language:	Czech, English
Teaching methods:	full-time
Additional information:	http://utf.mff.cuni.cz/vyuka/NTMF022

Guarantor:	RNDr. Jiří Novotný, CSc.
Teacher(s):	RNDr. Jiří Novotný, CSc.
Classification:	Physics > Theoretical and Math. Physics
Comes under:	Doporučené přednášky 1/2

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Annotation -

Gauge invariance, quantization of gauge fields, renormalization and renormalization group, spontaneous symmetry breaking, gauge theories in particle physics, the standard model. For the 2nd year of the Thoeretical Physics and Particle and Nuclear Physics studies and postgraduate students.

Last update: Krtička Milan, doc. Mgr., Ph.D. (29.04.2019)

Course completion requirements - Czech

Ústní zkouška

Last update: Houfek Karel, doc. RNDr., Ph.D. (11.06.2019)

Literature -

L. D. Faddeev, A.A. Slavnov, Gauge fileds, Introduction to quantum theory, Adisson-Wesley Publishing Company, 1991

S. Weinberg, The quantum theory of fields II, Cambridge University Press, 1996

K. Huang, Quarks, leptons and gauge fields, World Scientific 1982

C. Itzykcon, J.-B. Zuber, Quantum field theory, McGraw-Hill 1980

M. Heneaux, C. Teitelboim, Quantization of gauge systems, Princeton University Press, 1991

Last update: T_UCJF (19.03.2015)

Requirements to the exam - Czech

Zkouška bude ústní, požadavky odpovídají odpřednášené části sylabu, ev. doplněné o část zadanou k samostatnému nastudování.

Last update: Novotný Jiří, RNDr., CSc. (13.10.2017)

Syllabus -

1. Gauge invariance.

Electromagnetic fields, U(1) gauge transformations. Yang-Mills fields, non-abelian gauge group, parallel transport, covariant derivative, intensity tensor, Wilson loop. Invariant Lagrangians, scalar and spinor fields.

2. Classical solutions

Equations of motion, Bianchi identities. Hamilton formalism, Gauss law. Classical solutions in Minkowski regime, (non)existence of soliton solutions. Classical solutions in the Euclidean regime, instantons.

3. Quantization of gauge fields

Hamiltonian systems with constraints, Dirac quantization. Functional integral, gauge fixation, Faddeev-Popov ghosts, Feynman rules. BRST symmetry. Batalin-Vilkovisky method.

4. Renormalization of gauge theories

UV divergences, regularization, renormalization. Renormalizability of gauge theories, anomalies. Renormalization group, asymptotic freedom.

5. Spontaneous gauge symmetry breaking

Spontaneous global symmetry breaking, Goldstone theorem. Spontaneous local symmetry breaking, Higgs mechanism. Dynamical gauge symmetry breaking.

6. Gauge theories in particle physics

Quantum chromodynamics. The Standard Model of electroweak interactions. Grand unification theory.

Last update: T_UTF (15.05.2012)