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Course, academic year 2023/2024
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Batalin-Vilkovisky formalism - NMAG661
Title: Batalin-Vilkoviského formalismus
Guaranteed by: Mathematical Institute of Charles University (32-MUUK)
Faculty: Faculty of Mathematics and Physics
Actual: from 2020
Semester: winter
E-Credits: 3
Hours per week, examination: winter s.:2/0, Ex [HT]
Capacity: unlimited
Min. number of students: unlimited
4EU+: no
Virtual mobility / capacity: no
State of the course: not taught
Language: Czech, English
Teaching methods: full-time
Teaching methods: full-time
Guarantor: prof. Ing. Branislav Jurčo, CSc., DSc.
Class: DS, geom. a topologie, gl. analýza a ob. struktury
M Mgr. MSTR > Volitelné
Classification: Mathematics > Mathematics General
Physics > Theoretical and Math. Physics
Annotation -
Batalin-Vilkovisky formalism is used in theory of operads and in gauge theories. We shall introduce the BRST and BV formalisms. The course is aimed at Masters and PhD students of mathematics and physics.
Last update: Šmíd Dalibor, Mgr., Ph.D. (12.05.2018)
Course completion requirements -

Oral examination.

Last update: Šmíd Dalibor, Mgr., Ph.D. (28.10.2019)
Literature -

Joaquim Gomis, Jordi Paris, Stuart Samuel, Antibracket, Antifields and Gauge-Theory Quantization, Phys.Rept. 259 (1995) 1-145

Albert Schwarz, Geometry of Batalin-Vilkovisky quantization, Commun.Math.Phys. 155 (1993) 249-260

Marc Henneaux, Claudio Teitelboim, M.Quantization of Gauge Systems, Princeton University Press, 1994

Alexandrov, M. Kontsevich, A. Schwarz, O. Zaboronsky, The Geometry of the Master Equation and Topological Quantum Field Theory, Int.J.Mod.Phys. A12 (1997) 1405-1430

Steven Weinberg, The Quantum Theory of Fields, Volume 2: Modern Applications, Cambridge University Press, 2005

ALBERTO S. CATTANEO and FLORIAN SCHÄTZ, INTRODUCTION TO SUPERGEOMETRY, Rev. Math. Phys. 23, 669 (2011)

Kevin Costello, Renormalization and Effective Field Theory, American Mathematical Society, 2011

Bertram Kostant, Shlomo Sternberg, Symplectic reduction, BRS cohomology, and infinite-dimensional Clifford algebras, Annals of Physics, Volume 176, Issue 1, 15 May 1987, Pages 49-113

Last update: Jurčo Branislav, prof. Ing., CSc., DSc. (28.06.2018)
Teaching methods -

Guided reading, presenations by participants

Last update: Jurčo Branislav, prof. Ing., CSc., DSc. (28.10.2019)
Requirements to the exam -

The questions during an oral exam will concern the most iportant parts of the subject. Further details will be specified during the semester.

Last update: Jurčo Branislav, prof. Ing., CSc., DSc. (28.10.2019)
Syllabus -

Graded manifolds, integartion on superspaces, homotopy Lie algebras, Mauer-Cartan euqation, BRST, BV path integral, geometry of BV quantization, Effective action, minimal models

Last update: Jurčo Branislav, prof. Ing., CSc., DSc. (14.05.2019)
 
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