Jump to ContentJump to Main Navigation
Show Summary Details
More options …

Georgian Mathematical Journal

Editor-in-Chief: Kiguradze, Ivan / Buchukuri, T.

Editorial Board: Kvinikadze, M. / Bantsuri, R. / Baues, Hans-Joachim / Besov, O.V. / Bojarski, B. / Duduchava, R. / Engelbert, Hans-Jürgen / Gamkrelidze, R. / Gubeladze, J. / Hirzebruch, F. / Inassaridze, Hvedri / Jibladze, M. / Kadeishvili, T. / Kegel, Otto H. / Kharazishvili, Alexander / Kharibegashvili, S. / Khmaladze, E. / Kiguradze, Tariel / Kokilashvili, V. / Krushkal, S. I. / Kurzweil, J. / Kwapien, S. / Lerche, Hans Rudolf / Mawhin, Jean / Ricci, P.E. / Tarieladze, V. / Triebel, Hans / Vakhania, N. / Zanolin, Fabio


IMPACT FACTOR 2018: 0.551

CiteScore 2018: 0.52

SCImago Journal Rank (SJR) 2018: 0.320
Source Normalized Impact per Paper (SNIP) 2018: 0.711

Mathematical Citation Quotient (MCQ) 2018: 0.27

Online
ISSN
1572-9176
See all formats and pricing
More options …
Volume 26, Issue 2

Issues

L in physics and in Georgia

Jim Stasheff
  • Corresponding author
  • Department of Mathematics, University of North Carolina at Chapel Hill UNC-CH, Chapel Hill, NC 27599-3250, USA
  • Email
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
Published Online: 2019-05-16 | DOI: https://doi.org/10.1515/gmj-2019-2019

Abstract

Here is a sketch of a few of the connections between Prof. Nodar Berikashvili and his school and higher homotopy structures.

Keywords: Twisting cochains; cohomological physics; higher homotopy structures

MSC 2010: 55P62; 55R20; 55U99; 81T13

Dedicated to the 90th birthday of Nodar Berikashvili

References

  • [1]

    I. A. Batalin and E. S. Fradkin, A generalized canonical formalism and quantization of reducible gauge theories, Phys. Lett. B 122 (1983), no. 2, 157–164. CrossrefGoogle Scholar

  • [2]

    I. A. Batalin and G. A. Vilkovisky, Quantization of gauge theories with linearly dependent generators, Phys. Rev. D (3) 28 (1983), no. 10, 2567–2582; Erratum: Phys. Rev. D (3) 30 (1984), no. 2, 508. CrossrefGoogle Scholar

  • [3]

    I. A. Batalin and G. A. Vilkovisky, Closure of the gauge algebra, generalized Lie equations and Feynman rules, Nuclear Phys. B 234 (1984), no. 1, 106–124. CrossrefGoogle Scholar

  • [4]

    I. A. Batalin and G. A. Vilkovisky, Existence theorem for gauge algebra, J. Math. Phys. 26 (1985), no. 1, 172–184. CrossrefGoogle Scholar

  • [5]

    C. Becchi, A. Rouet and R. Stora, Renormalization of the abelian Higgs–Kibble model, Comm. Math. Phys. 42 (1975), 127–162. CrossrefGoogle Scholar

  • [6]

    F. A. Berends, G. J. H. Burgers and H. van Dam, On the theoretical problems in constructing interactions involving higher-spin massless particles, Nuclear Phys. B 260 (1985), no. 2, 295–322. CrossrefGoogle Scholar

  • [7]

    F. A. Berends, G. J. H. Burgers and H. van Dam, Explicit construction of conserved currents for massless fields of arbitrary spin, Nuclear Phys. B 271 (1986), no. 2, 429–441. CrossrefGoogle Scholar

  • [8]

    A. D. Browning and D. McMullan, The Batalin, Fradkin, and Vilkovisky formalism for higher-order theories, J. Math. Phys. 28 (1987), no. 2, 438–444. CrossrefGoogle Scholar

  • [9]

    G. J. H. Burgers, On the construction of field theories for higher spin massless particles, Ph.D. thesis, Rijksuniversiteit te Leiden, 1985. Google Scholar

  • [10]

    C. Chevalley and S. Eilenberg, Cohomology theory of Lie groups and Lie algebras, Trans. Amer. Math. Soc. 63 (1948), 85–124. CrossrefGoogle Scholar

  • [11]

    L. D. Faddeev and V. N. Popov, Feynman diagrams for the Yang–Mills field, Phys. Lett. B 25 (1967), 29–30. CrossrefGoogle Scholar

  • [12]

    E. S. Fradkin and T. E. Fradkina, Quantization of relativistic systems with boson and fermion first and second class constraints, Phys. Lett. B 72 (1978), no. 3, 343–348. CrossrefGoogle Scholar

  • [13]

    E. S. Fradkin and G. A. Vilkovisky, Quantization of relativistic systems with constraints, Phys. Lett. B 55 (1975), no. 2, 224–226. CrossrefGoogle Scholar

  • [14]

    R. Fulp, T. Lada and J. Stasheff, sh-Lie algebras induced by gauge transformations, Comm. Math. Phys. 231 (2002), no. 1, 25–43. CrossrefGoogle Scholar

  • [15]

    M. Henneaux, Hamiltonian form of the path integral for theories with a gauge freedom, Phys. Rep. 126 (1985), no. 1, 1–66. CrossrefGoogle Scholar

  • [16]

    O. Hohm and B. Zwiebach, L algebras and field theory, Fortschr. Phys. 65 (2017), no. 3–4, Article ID 1700014. Google Scholar

  • [17]

    T. Lada and J. Stasheff, Introduction to SH Lie algebras for physicists, Internat. J. Theoret. Phys. 32 (1993), no. 7, 1087–1103. CrossrefGoogle Scholar

  • [18]

    C. Nash, Topology and physics—a historical essay, History of Topology, North-Holland, Amsterdam (1999), 359–415. Google Scholar

  • [19]

    A. Nützi and M. Reiterer, Scattering amplitudes in YM and GR as minimal model brackets and their recursive characterization, preprint (2018), https://arxiv.org/abs/1812.06454.

  • [20]

    R. Stora, Continuum gauge theories, New Developments in Quantum Field Theory and Statistical Mechanics (Cargèse 1976), NATO Adv. Study Inst. Ser. Ser. B: Physics 26, Plenum, New York (1977), 201–224. Google Scholar

  • [21]

    D. Sullivan, Infinitesimal computations in topology, Inst. Hautes Études Sci. Publ. Math. (1977), no. 47, 269–331. Google Scholar

  • [22]

    I. V. Tyutin, Gauge invariance in field theory and statistical physics in operator formulation (in Russian), Technical report, Lebedev Physics Institut, 1975. Google Scholar

  • [23]

    B. Zwiebach, Closed string field theory: Quantum action and the Batalin–Vilkovisky master equation, Nuclear Phys. B 390 (1993), no. 1, 33–152. CrossrefGoogle Scholar

About the article

Received: 2018-09-30

Accepted: 2019-01-13

Published Online: 2019-05-16

Published in Print: 2019-06-01


Citation Information: Georgian Mathematical Journal, Volume 26, Issue 2, Pages 311–314, ISSN (Online) 1572-9176, ISSN (Print) 1072-947X, DOI: https://doi.org/10.1515/gmj-2019-2019.

Export Citation

© 2019 Walter de Gruyter GmbH, Berlin/Boston.Get Permission

Comments (0)

Please log in or register to comment.
Log in