Advanced Concepts of Symmetry - NJSF129

• Title: Pokročilé koncepty symetrie
• Guaranteed by: Institute of Particle and Nuclear Physics (32-UCJF)
• Faculty: Faculty of Mathematics and Physics
• Actual: from 2015 to 2017
• 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: English
• Teaching methods: full-time
• Teaching methods: full-time
• Guarantor: prof. Alfredo Iorio, Ph.D.
• Classification: Physics > Nuclear and Subnuclear Physics
• Comes under: Doporučené přednášky 2/2

Annotation

English

Last update: T_UCJF (13.05.2008)

The goal of these lectures is to give as much a unified view as possible of the different kinds of symmetries (either solidly tested or simply speculated) encountered in field theory.

Czech

Last update: T_UCJF (13.05.2008)

Cílem prednášky je poskytnout ucelený pohled na ruzné druhy symetrií (jak overených, tak i preppokládaných) vyskytujících se v teorii pole.

Syllabus

English

Last update: doc. Mgr. Milan Krtička, Ph.D. (30.04.2019)

Important concepts and mathematical structures - such as the conformal and the super symmetry algebras, central charges and topological objects - and their role in classical and quantum field theories and solid state physics will be introduced.

Special emphasis will be given to topological objects in the framework of gauge theories of the Yang-Mills type and of the Chern-Simons type, and in the framework of gravity theories in three and lower dimensions.

The course is divided in three parts:

PART I: Noether charges and Supersymmetry.

The Noether theorem for classical field theories will be presented and discussed in general. Spatiotemporal symmetries from the conformal symmetry to supersymmetry will be introduced. The latter will be achieved via the Haag-Lopuszanski-Sohnius construction of the SUSY algebra.

PART II: Topological objects in gauge theories.

Conservation laws not descending from the Noether theorem will be presented. Important topological objects such as Dirac and 't Hooft-Polyakov monopoles and topological gauge theories, such as the Chern-Simons theory, will be discussed.

PART III: Topological objects in gravity theories.

Three dimensional Einstein gravity will be shown to be equivalent to a gauge theory of the Chern-Simons type. The Chern-Simons gravitational term (conformal gravity) will be presented.

Applications of all the above to condensed matter systems could be outlined.

Bibliography:

[1] A. Iorio, Lecture notes, 2009.

[2] L. H. Ryder, Quantum Field Theory, Cambridge Univ. Press, 1985.

[3] S. Weinberg, The Quantum Theory of Fields, Cambridge Univ. Press,

1995 (Vols. 2 and 3).

[4] J. D. Walecka, Advanced Modern Physics, World Scientific, 2010.

[5] A. Altland, B. Simons, Condensed Matter Field Theory, Cambridge

Univ. Press, 2006.

[6] S. Coleman, Aspects of Symmetry, Cambridge Univ. Press, 1985.

[7] R. Jackiw, Diverse topics in Theoretical and Mathematical Physics,

World Scientific, 1995.

[8] C. Nash, S. Sen, Topology for physicists, Academic Press,1988.

[9] M. Nakahara, Geometry, Topology and Physics, IOP Publ., 1990.

[10] J. Wess, J. Bagger, Supersymmetry and Supergravity, Princeton

Univ. Press, 1992.

[11] S. Carlip, Quantum Gravity in 2+1 Dimensions, Cambridge Univ.

Press, 2003.

Czech

Last update: doc. Mgr. Milan Krtička, Ph.D. (30.04.2019)

Rozdíly mezi časoprostorovými a vnitřními

symetriemi (na úrovni teoremu Noetherové pro klasická pole

ve čtyřech dimenzích) a dvěma přístupy (obecná relativita ve

třech dimenzích a supersymetrie)

v nichž byly tyto symetrie sjednoceny.

Supersymetrie bude zkoumána způsobem, který se nevyskytuje v tradiční

literatuře.

Vytvoření superalgebry a jejích reprezentací skýtá možnost podívat se

na další projevy symetrií jako jsou centrální náboje, monopóly a

obecně BPS stavy.

Po diskusi rozšíření Lorentzovy invariance na supersymetrii se budeme

zabývat možnými projevy narušení této invariance v rámci nekomutativní

teorie pole.

[1] A. Iorio, Lecture notes, 2009.

[2] L. H. Ryder, Quantum Field Theory, Cambridge Univ. Press, 1985.

[3] S. Weinberg, The Quantum Theory of Fields, Cambridge Univ. Press,

1995 (Vols. 2 and 3).

[4] J. D. Walecka, Advanced Modern Physics, World Scientific, 2010.

[5] A. Altland, B. Simons, Condensed Matter Field Theory, Cambridge

Univ. Press, 2006.

[6] S. Coleman, Aspects of Symmetry, Cambridge Univ. Press, 1985.

[7] R. Jackiw, Diverse topics in Theoretical and Mathematical Physics,

World Scientific, 1995.

[8] C. Nash, S. Sen, Topology for physicists, Academic Press,1988.

[9] M. Nakahara, Geometry, Topology and Physics, IOP Publ., 1990.

[10] J. Wess, J. Bagger, Supersymmetry and Supergravity, Princeton

Univ. Press, 1992.

[11] S. Carlip, Quantum Gravity in 2+1 Dimensions, Cambridge Univ.

Press, 2003.