И. Л. Бухбиндер1,2,3,a, С. А. Федорук1,b, В. А. Крыхтин2,4,c
Ключевые слова:
высшие спины, БРСТ-формулировка
Категории:
Физика
, Физика высоких энергий (теория)
Аннотация
Мы даем краткий обзор БРСТ-подхода к калибровочно-инвариантной лагранжевой формулировке для свободных массивных бозонных полей высших спинов, акцентируя внимание на двух специфических аспектах. Во-первых, теория рассматривается в четырехмерном плоском пространстве в терминах спин-тензорных полей с двухкомпонентными неточечными и точечными индексами. Это приводит к существенному упрощению всего подхода по сравнению с тем, где использовались поля с векторными индексами, поскольку теперь нет необходимости вводить в БРСТ-заряд связь, отвечающую за следы полей. Во-вторых, мы разрабатываем предельно простую и наглядную процедуру для исключения всех вспомогательных полей и доказываем, что БРСТ-уравнения движения тождественно воспроизводят основные условия для неприводимых представлений группы Пуанкаре с заданной массой и спином. Подобно безмассовой теории, окончательный лагранжиан для массивных полей высших спинов формулируется в триплетной форме. БРСТ-формулировка приводит к системе полей, которые четко подразделяются на основное поле спина s, вспомогательные поля типа Зиновьева, вспомогательные поля типа Сингха–Хагена и специальные вспомогательные БРСТ-поля. Вспомогательные поля могут быть частично устранены путем фиксации калибровки и/или с помощью уравнений движения. Это позволяет получить формально разные (с разным числом вспомогательных полей), но эквивалентные лагранжевы формулировки.
Библиографические ссылки
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[27] I. L. Buchbinder, V. A. Krykhtin, Gauge invariant Lagrangian construction for massive bosonichigher spin fields in D dimensions, Nuclear Physics B 727 (2005) 537.arXiv:hep-th/0505092.
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[29] I. L. Buchbinder, V. A. Krykhtin, H. Takata, Gauge invariant Lagrangian construction for massivebosonic mixed symmetry higher spin fields, Physics Letters B 656 (2007) 253.arXiv:0707.2181[hep-th].
[30] I. L. Buchbinder, A. V. Galajinsky, Quartet unconstrained formulation for massive higher spinfields, Journal of High Energy Physics 11 (2008) 081,arXiv:0810.2852 [hep-th].
[31] A. I. Pashnev, Composite systems and field theory for a free Regge trajectory, Theoretical andMathematical Physics 78 (1989) 272.
[32] A. Pashnev, M. Tsulaia, Dimensional reduction and the BRST approach to the description of aRegge trajectory, Modern Physics Letters A 12 (1997) 861.arXiv:hep-th/9703010.
[33] X. Bekaert, I. L. Buchbinder, A. Pashnev, M. Tsulaia, On higher spin theory: Strings, BRST,dimensional reduction, Classical and Quantum Gravity 21 (2004) S1457.arXiv:hep-th/0312252.
[34] M. A. Vasiliev, Supersymmetric higher-spin gauge theories in anydand their coupling constantswithin BRST formalism.arXiv:2503.10967 [hep-th].
[35] M. V. Khabarov, Yu. M. Zinoviev, Massive higher spin fields in the frame-like multispinor formal-ism, Nuclear Physics B 948 (2019) 11477.arXiv:1906.03438 [hep-th].
[36] I. L. Buchbinder, K. Koutrolikos, BRST analysis of the supersymmetric higher spin field models,Journal of High Energy Physics 12 (2015) 106.arXiv:1510.06569 [hep-th].
[37] I. L. Buchbinder, S. A. Fedoruk, A. P. Isaev, V. A. Krykhtin, On BRST Lagrangian formulation ofmassless higher spin fields, Russian Physics Journal 67 (2024) 1806.arXiv:2412.08298 [hep-th].
[38] I. L. Buchbinder, S. V. Kuzenko, Ideas and methods of supersymmetry and supergravity, or awalk through superspace, IOP Publishing, Bristol and Philadelphia, 1995; Revised Edition, 1998.
[39] L. D. Faddeev, S. L. Shatashvili, Realization of the Schwinger term in the Gauss law and thepossibility of correct quantization of a theory with anomalies, Physics Letters B 167 (1986) 225.
[40] I. A. Batalin, E. S. Fradkin, Operatorial quantization of dynamical systems subject to second-classconstraints, Nuclear Physics B 279 (1987) 514.
[41] I. L. Buchbinder, V. A. Krykhtin, H. Takata, BRST approach to Lagrangian construction fo
[2] X. Bekaert, S. Cnockaert, C. Iazeolla, M. A. Vasiliev, Nonlinear higher spin theories in variousdimensions, in: Higher spin gauge theories: Proceedings, 1st Solvay Workshop: Brussels, Belgium,12–14 May, 2004, pp. 132–197.arXiv:hep-th/0503128.
[3] A. Fotopoulos, M. Tsulaia, Gauge-invariant Lagrangians for free and interacting higher spin fields:A review of the BRST formulation, International Journal of Modern Physics A 24 (2009) 1.arXiv:0805.1346 [hep-th].
[4] X. Bekaert, N. Boulanger, P. Sundell, How higher spin gravity surpasses the spin two barrier: No-go theorems versus yes-go examples, Reviews of Modern Physics 84 (2012) 987.arXiv:1007.0435[hep-th].
[5] V. E. Didenko, E. D. Skvortsov, Elements of Vasiliev theory.arXiv:1401.2975 [hep-th].
[6] M. A. Vasiliev, Higher-spin theory and space-time metamorphoses, Lecture Notes in Physics 892(2015) 227.arXiv:1404.1948 [hep-th].
[7] X. Bekaert, E. D. Skvortsov, Elementary particles with continuous spin, International Journal ofModern Physics A 32 (2017) 1730019.arXiv:1708.01030 [hep-th].
[8] X. Bekaert, N. Boulanger, A. Campaneoli, M. Chodaroli, D. Francia, M. Grigoriev, E. Sez-gin, E. Skvortsov, Snowmass White Paper: Higher spin gravity and higher spin symmetry.arXiv:2205.01567 [hep-th].
[9] D. Ponomarev, Basic introduction to higher-spin theories.arXiv:2206.15385 [hep-th].
[10] A. Ochirov, E. Skvortsov, Chiral approach to massive higher spins, Physical Review Letters 129(2022) 125027,arXiv:2207.14597 [hep-th].
[11] L. W. Lindwasser, Consistent actions for massive particles interacting with electromagnetism andgravity, Journal of High Energy Physics 08 (2024) 081.arXiv:2309.03901 [hep-th].
[12] J. H. Fegebank, S. M. Kuzenko, Quantisation of the gauge-invariant models for massive higher-spinbosonic fields.arXiv:2310.00951 [hep-th].
[13] E. Skvortsov, M. Tsulaia, Cubic action for spinning black holes from massive higher-spin gaugesymmetry, Journal of High Energy Physics 02 (2024) 202.arXiv:2312.08184 [hep-th].
[14] A. J. Fegebank, S. M. Kuzenko, Equivalence of gauge-invariant models for massive integer-spinfields, Physical Review D 110 (2024) 10, 105014.arXiv:2406.02573 [hep-th].
[15] W. Delplanque, E. Skvortsov, Symmetric vs. chiral approaches to massive fields with spin, Classicaland Quantum Gravity 41 (2024) 24, 245018.arXiv:2405.13706 [hep-th].[16] W. Delplanque, E. Skvortsov, Massive spin three-half field in a constant electromagnetic back-ground, Journal of High Energy Physics 08 (2024) 173,arXiv:2406.14148 [hep-th].
[17] W. Delplanque, All actions for free massive higher-spin fields, Physical Review D 111 (2025) 4.arXiv:2411.03463 [hep-th].
[18] L. F. S. Singh, C. R. Hagen, Lagrangian formulation for arbitrary spin: 1. The bosonic case,Physical Review D 9 (1974) 898.
[19] L. F. S. Singh, C. R. Hagen, Lagrangian formulation for arbitrary spin: 2. The fermionic case,Physical Review D 9 (1974) 910.
[20] J. Schwinger, Particles, Sources and Fields, Vol. 1, Addison-Wesley Publishing Company, 1970,426 pp.
[21] M. Fierz and W. Pauli, On relativistic wave equations for particles of arbitrary spin in an elec-tromagnetic field, Proceedings of the Royal Society of London A 173 (1939) 211.
[22] Yu. M. Zinoviev, Gauge invariant description of massive high spin particle, Serpukhov, Instituteof High Energy Physics, report number: IFVE-83-91,1983.
[23] S. M. Klishevich, Yu. M. Zinovev, On electromagnetic interaction of massive spin-2 particle,Physics of Atomic Nuclei 61 (1998) 1527.arXiv:hep-th/9708150.
[24] Yu. M. Zinoviev, On massive higher-spin particles in AdS.arXiv:hep-th/0108192.
[25] R. R. Metsaev, Massive totally symmetric fields in AdS(d), Physics Letters B 590 (2004) 95.arXiv:hep-th/0312297 [hep-th].
[26] R. R. Metsaev, Gauge invariant formulation of massive totally symmetric fermionic fields in (A)dSspace, Physics Letters B 643 (2006) 205.arXiv:hep-th/0609029 [hep-th].
[27] I. L. Buchbinder, V. A. Krykhtin, Gauge invariant Lagrangian construction for massive bosonichigher spin fields in D dimensions, Nuclear Physics B 727 (2005) 537.arXiv:hep-th/0505092.
[28] I. L. Buchbinder, V. A. Krykhtin, P. M. Lavrov, Gauge invariant Lagrangian formulation ofhigher spin massive bosonic field theory in AdS space, Nuclear Physics B 762 (2006) 386.arXiv:hep-th/0608005.
[29] I. L. Buchbinder, V. A. Krykhtin, H. Takata, Gauge invariant Lagrangian construction for massivebosonic mixed symmetry higher spin fields, Physics Letters B 656 (2007) 253.arXiv:0707.2181[hep-th].
[30] I. L. Buchbinder, A. V. Galajinsky, Quartet unconstrained formulation for massive higher spinfields, Journal of High Energy Physics 11 (2008) 081,arXiv:0810.2852 [hep-th].
[31] A. I. Pashnev, Composite systems and field theory for a free Regge trajectory, Theoretical andMathematical Physics 78 (1989) 272.
[32] A. Pashnev, M. Tsulaia, Dimensional reduction and the BRST approach to the description of aRegge trajectory, Modern Physics Letters A 12 (1997) 861.arXiv:hep-th/9703010.
[33] X. Bekaert, I. L. Buchbinder, A. Pashnev, M. Tsulaia, On higher spin theory: Strings, BRST,dimensional reduction, Classical and Quantum Gravity 21 (2004) S1457.arXiv:hep-th/0312252.
[34] M. A. Vasiliev, Supersymmetric higher-spin gauge theories in anydand their coupling constantswithin BRST formalism.arXiv:2503.10967 [hep-th].
[35] M. V. Khabarov, Yu. M. Zinoviev, Massive higher spin fields in the frame-like multispinor formal-ism, Nuclear Physics B 948 (2019) 11477.arXiv:1906.03438 [hep-th].
[36] I. L. Buchbinder, K. Koutrolikos, BRST analysis of the supersymmetric higher spin field models,Journal of High Energy Physics 12 (2015) 106.arXiv:1510.06569 [hep-th].
[37] I. L. Buchbinder, S. A. Fedoruk, A. P. Isaev, V. A. Krykhtin, On BRST Lagrangian formulation ofmassless higher spin fields, Russian Physics Journal 67 (2024) 1806.arXiv:2412.08298 [hep-th].
[38] I. L. Buchbinder, S. V. Kuzenko, Ideas and methods of supersymmetry and supergravity, or awalk through superspace, IOP Publishing, Bristol and Philadelphia, 1995; Revised Edition, 1998.
[39] L. D. Faddeev, S. L. Shatashvili, Realization of the Schwinger term in the Gauss law and thepossibility of correct quantization of a theory with anomalies, Physics Letters B 167 (1986) 225.
[40] I. A. Batalin, E. S. Fradkin, Operatorial quantization of dynamical systems subject to second-classconstraints, Nuclear Physics B 279 (1987) 514.
[41] I. L. Buchbinder, V. A. Krykhtin, H. Takata, BRST approach to Lagrangian construction fo