pith. sign in

arxiv: 2606.24008 · v1 · pith:FUCJDWQCnew · submitted 2026-06-22 · ✦ hep-th · math-ph· math.DS· math.MP· math.RT

General Lagrangian formulations for mixed-antisymmetric tensor fields on flat backgrounds

Alexander A. Reshetnyak This is my paper

Pith reviewed 2026-06-26 06:54 UTC · model grok-4.3

classification ✦ hep-th math-phmath.DSmath.MPmath.RT
keywords higher-spin fieldsmixed-antisymmetric tensorsYoung tableauxBRST formalismconstraint conversionPoincaré representationsgauge-invariant Lagrangians
0
0 comments X

The pith

BRST constraint conversion produces Lagrangian formulations for mixed-antisymmetric higher-spin fields with arbitrary Young symmetry.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper constructs Lagrangian descriptions for massless and massive integer higher-spin particles whose field content is fixed by a Young tableau with k columns of antisymmetric indices. It begins with a Fock-space realization of the Poincaré module and converts the original second-class operator constraints into first-class ones by adjoining auxiliary oscillator variables whose algebra is isomorphic to so(k,k). Both an unconstrained formulation using the full BRST operator Q and a constrained formulation using the incomplete operator Qc plus algebraic constraints are obtained; the two versions have equivalent dynamics but differ in their configuration spaces. The construction applies uniformly to all such (ir)reducible representations in flat d-dimensional space-time.

Core claim

Lagrangian formulations for (ir)reducible integer higher-spin massless and massive Poincaré group representations subject to Young tableau with k columns Y[ŝ1,ŝ2,...,ŝk] are obtained by realizing the fields in an auxiliary Fock space, locating auxiliary representations of the constraint subalgebra via Verma modules that are isomorphic to so(k,k) by Howe duality, and thereby converting the initial second-class operator constraints into a first-class system; both unconstrained (with Q) and constrained (with Qc) gauge-invariant actions with equivalent dynamics result.

What carries the argument

BRST conversion of second-class constraints via auxiliary Fock modules isomorphic to so(k,k) through Howe duality and Verma-module construction.

If this is right

  • The same conversion supplies gauge-invariant actions for both massless and massive mixed-antisymmetric fields of any column number k.
  • Unconstrained and constrained versions exist side by side, differing only in the size of the configuration space.
  • The method supplies a uniform starting point for studying consistent interactions among these fields.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The construction may serve as a template for extending the same constraint-conversion technique to fields on curved backgrounds.
  • The appearance of an so(k,k) algebra suggests possible links to other algebraic structures that appear in higher-spin theory.

Load-bearing premise

The auxiliary so(k,k) representations convert the second-class operators into first-class ones while leaving the physical dynamics unchanged.

What would settle it

An explicit check for a low-spin case (such as k=2, spin 2) in which the equations derived from the converted BRST action fail to match the original Fronsdal or symmetric-tensor equations of motion.

read the original abstract

Lagrangian formulations for (ir)reducible integer higher-spin massless and massive Poincare group representations subject to Young tableau with $k$ columns $Y[\hat{s}_1,\hat{s}_2,...,\hat{s}_k]$ in $d$-dimensional Minkowski space-time are firstly presented. The particles are described in a metric-like formulation by tensor fields with $k$ groups of antisymmetric Lorentz indices $\Phi_{\mu^1[{\hat{s}_1}],\mu^2[{\hat{s}_2}],..., \mu^k[{\hat{s}_k}]}$ by means of the BRST procedure with complete, $Q$, and incomplete, $Q_c$, BRST operators. Starting from a description of bosonic mixed-antisymmetric higher-spin fields in terms of an auxiliary Fock space associated with a special Poincare module, we realize a conversion of the initial operator constraint system into a system of first-class operator constraints. To this aim, we find, in first time, by means of Verma module the auxiliary representations of the constraint subalgebra, to be isomorphic due to Howe duality to $so(k,k)$ algebra, and containing the subsystem of second-class operators in terms of new oscillator variables forming the Fock module. An unconstrained (with $Q$) and constrained (with $Q_c$ and BRST invariant algebraic constraints) gauge Lagrangian formulations with equivalent dynamics, but different configuration spaces are found. Concept of consistent interactions are suggested.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

0 major / 2 minor

Summary. The paper claims to present the first general Lagrangian formulations for (ir)reducible integer higher-spin massless and massive Poincaré representations labeled by Young tableaux with k columns Y[ŝ₁, ŝ₂, ..., ŝₖ] in d-dimensional Minkowski spacetime. Fields are described in metric-like form by tensors with k groups of antisymmetric indices via the BRST procedure, converting the initial second-class operator constraints into first-class ones using auxiliary Fock modules constructed from Verma modules (isomorphic to so(k,k) by Howe duality). This yields both an unconstrained formulation (complete BRST operator Q) and a constrained formulation (incomplete Qc plus BRST-invariant algebraic constraints) asserted to have equivalent dynamics, with a suggestion for consistent interactions.

Significance. If the constructions and claimed dynamical equivalence hold, the work supplies a systematic BRST-based framework for mixed-antisymmetric higher-spin fields that extends prior treatments of totally symmetric and other mixed-symmetry cases. The explicit use of Verma modules and Howe duality to realize the auxiliary representations, together with the provision of both complete and incomplete BRST Lagrangians, constitutes a technical advance that could facilitate studies of interactions and reducible representations.

minor comments (2)
  1. [Abstract] Abstract: the phrasing 'firstly presented' and 'in first time' should be supported in the introduction by explicit citations to the most closely related prior BRST constructions for mixed-symmetry fields (e.g., those using similar constraint-conversion techniques).
  2. The manuscript should include at least one explicit low-rank example (e.g., k=2, small ŝᵢ) with the resulting Lagrangian written out in components to illustrate the general formulae.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the positive assessment of the manuscript and the recommendation for minor revision. No specific major comments appear in the report, so we have no individual points requiring detailed rebuttal or clarification.

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The paper constructs Lagrangian formulations via the BRST procedure applied to auxiliary Fock modules obtained from Verma modules, using the standard isomorphism to so(k,k) under Howe duality to convert second-class constraints to first-class ones. This follows established techniques in higher-spin field theory without any quoted step reducing a claimed prediction or result to a fitted parameter, self-definition, or load-bearing self-citation chain. The abstract and described procedure contain no equations or definitions that are equivalent to their inputs by construction. The derivation is self-contained against external benchmarks from representation theory and BRST formalism.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

Based on abstract only; relies on standard assumptions of Poincare representations, Young tableaux, and BRST constraint conversion without new free parameters or invented entities visible.

axioms (2)
  • domain assumption Poincare group representations labeled by Young tableaux with k columns describe the higher-spin fields
    Invoked as the starting point for the tensor field description.
  • domain assumption BRST procedure with auxiliary Fock space converts second-class constraints to first-class ones
    Core technical step claimed to enable the Lagrangian formulations.

pith-pipeline@v0.9.1-grok · 5805 in / 1189 out tokens · 34233 ms · 2026-06-26T06:54:24.407794+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

111 extracted references · 47 linked inside Pith

  1. [1]

    Vasiliev, Higher Spin Gauge Theories in Various Dimensions, Fortsch

    M. Vasiliev, Higher Spin Gauge Theories in Various Dimensions, Fortsch. Phys. 52 (2004) 702–717, [arXiv:hep-th/0401177]

    Pith/arXiv arXiv 2004

  2. [2]

    Vasiliev, Higher spin theory and space-time metamorphoses

    M.A. Vasiliev, Higher spin theory and space-time metamorphoses. Lect. Notes Phys. 892 (2015) 227, [arXiv:1404.1948[hep-th]]

    Pith/arXiv arXiv 2015

  3. [3]

    Ponomarev, Basic introduction to higher spin theories, Int

    D. Ponomarev, Basic introduction to higher spin theories, Int. J. Theor. Phys. 62(2023) 146

    2023

  4. [4]

    Bekaert, N

    X. Bekaert, N. Boulanger, A. Campaneoni, M. Chodaroli, D. Francia, M. Grigoriev, E. Sez- gin and E. Skvortsov, Snowmass white paper: higher spin gravity and higher spin symmetry. arXiv:2205.01567[hep-th] 33

    arXiv

  5. [5]

    Rep.175 (1989) 1

    Thorn C., String Field TheoryPhys. Rep.175 (1989) 1

    1989

  6. [6]

    Witten, Noncommutative Geometry and String Field Theory, Nucl

    E. Witten, Noncommutative Geometry and String Field Theory, Nucl. Phys. B268 (1986) 253

    1986

  7. [7]

    Siegel, Introduction to String Field Theory, Adv.Ser.Math.Phys.8 (1988) 1–244, [arXiv:hep-th/0107094]

    W. Siegel, Introduction to String Field Theory, Adv.Ser.Math.Phys.8 (1988) 1–244, [arXiv:hep-th/0107094]

    Pith/arXiv arXiv 1988

  8. [8]

    Sagnotti, M

    A. Sagnotti, M. Tsulaia, On higher spins and the tensionless limit of string theory, Nucl. Phys. B682 (2004) 83, [arXiv:hep-th/0311257]

    Pith/arXiv arXiv 2004

  9. [9]

    Arkani-Hamed, D.P

    N. Arkani-Hamed, D.P. Finkbeiner, T.R. Slatyer, N. Weiner, A theory of dark matter, Phys. Rev. D79 (2009) 015014, [arXiv:0810.0713[hep-ph]]

    Pith/arXiv arXiv 2009

  10. [10]

    Bertone, J

    J.de Swart, G. Bertone, J. van Dongen, How dark matter came to matter, Nat. Astron. 1 (2017) 59, [arXiv:1703.00013[astro-ph.CO]]

    Pith/arXiv arXiv 2017

  11. [11]

    E. Boos, V. Bunichev, M. Dubinin , L. Dudko, etc. CMS Collaboration, Search for dark matter production in association with a single top quark in proton-proton collisions at √s = 13 TeV JHEP 2025 (2025) 141

    2025

  12. [12]

    Adshead, K.D

    P. Adshead, K.D. Lozanov, Z.J. Weiner, Dark photon dark matter from an oscillating dilaton, Phys. Rev. D107 (2023) 8, 083519, [arXiv:2301.07718 [hep-ph]]

    arXiv 2023

  13. [13]

    Fotopoulos, M

    A. Fotopoulos, M. Tsulaia, Gauge Invariant Lagrangians for Free and Interacting Higher Spin Fields. A Review of the BRST formulation, Int. J. Mod. Phys. A24 (2009) 1, [arXiv:0805.1346[hep-th]]

    Pith/arXiv arXiv 2009

  14. [14]

    Bengtsson,Higher Spin Field Theory (Texts and Monographs in Theoretical Physics)

    A. Bengtsson,Higher Spin Field Theory (Texts and Monographs in Theoretical Physics). Vol. 1, 2, (Berlin, 2023)

    2023

  15. [15]

    Singh, C.R

    L.P.S. Singh, C.R. Hagen, Lagrangian formulation for arbitrary spin. 1. The boson case, Phys. Rev. D9 (1974) 898

    1974

  16. [16]

    Fronsdal, Massless Fields with Integer Spin, Phys

    C. Fronsdal, Massless Fields with Integer Spin, Phys. Rev. D18 (1978) 3624

    1978

  17. [17]

    Fronsdal, Singletons and Massless, Integral Spin Fields on de Sitter Space (Elementary Particles in a Curved Space), Phys

    C. Fronsdal, Singletons and Massless, Integral Spin Fields on de Sitter Space (Elementary Particles in a Curved Space), Phys. Rev. D20 (1979) 848

    1979

  18. [18]

    Francia and A

    D. Francia and A. Sagnotti, Minimal Local Lagrangians for Higher-Spin Geometry, Phys. Lett. B.624 (2005) 93, [arXiv:hep-th/0507144]

    Pith/arXiv arXiv 2005

  19. [19]

    Buchbinder, A.V

    I.L. Buchbinder, A.V. Galajinsky, Quartet unconstrained formulation for massive higher spin fields, JHEP0811 (2008) 081, [arXiv:0810.2852[hep-th]]

    Pith/arXiv arXiv 2008

  20. [20]

    Buchbinder, V.A

    I.L. Buchbinder, V.A. Krykhtin, A.A. Reshetnyak Nucl. Phys. B787 (2007) 211, [arXiv:hep- th/0703049]

    arXiv 2007

  21. [21]

    Labastida, T.R

    J.M.F. Labastida, T.R. Morris, Massless mixed symmetry bosonic free fields, Phys. Lett. B180 (1986) 101

    1986

  22. [22]

    K. B. Alkalaev, O. V. Shaynkman, M. A. Vasiliev, On the frame - like formulation of mixed symmetry massless fields in (A)dS(d) Nucl. Phys. B692 (2004) 363, [arXiv:hep-th/0311164]. 34

    Pith/arXiv arXiv 2004

  23. [23]

    Alkalaev, O.V

    K.B. Alkalaev, O.V. Shaynkman and M.A. Vasiliev // JHEP. 0508 (2005) 069, [arXiv:hep- th/0501108]

    arXiv 2005

  24. [24]

    E. D. Skvortsov, Frame-like Actions for Massless Mixed-Symmetry Fields in Minkowski space, Nucl. Phys. B808 (2009) 569, [arXiv:0807.0903[hep-th]]

    Pith/arXiv arXiv 2009

  25. [25]

    Y. M. Zinoviev, Frame-like gauge invariant formulation for massive high spin particles, Nucl. Phys. B808 (2009) 185, [arXiv:0808.1778[hep-th]]

    Pith/arXiv arXiv 2009

  26. [26]

    Campoleoni, D

    A. Campoleoni, D. Francia, J. Mourad, A. Sagnotti, Unconstrained Higher Spins of Mixed Symmetry. I. Bose Fields, Nucl.Phys. B815 (2009) 289, [arXiv:0810.4350[hep-th]]

    Pith/arXiv arXiv 2009

  27. [27]

    Buchbinder, A.A

    I.L. Buchbinder, A.A. Reshetnyak, General Lagrangian Formulation for Higher Spin Fields with Arbitrary Index Symmetry. I. Bosonic fields, Nucl. Phys. B.862 (2012) 270, [arXiv:1110.5044[hep-th]]

    arXiv 2012

  28. [28]

    Reshetnyak, General Lagrangian Formulation for Higher Spin Fields with Arbitrary Index Symmetry

    A.A. Reshetnyak, General Lagrangian Formulation for Higher Spin Fields with Arbitrary Index Symmetry. II. Fermionic fields, Nucl. Phys. B.869 (2013) 523, [arXiv:1211.1273[hep- th]]

    arXiv 2013

  29. [29]

    Reshetnyak, P.Yu

    A.A. Reshetnyak, P.Yu. Moshin, Gauge Invariant Lagrangian Formulations for Mixed Symmetry Higher Spin Bosonic Fields in AdS Spaces, Universe 9 (2023) 495, [arXiv:2305.00142[hep-th]]

    arXiv 2023

  30. [30]

    Buchbinder, S

    I.L. Buchbinder, S. Fedoruk, A.P. Isaev, A. Rusnak, Model of massless relativistic par- ticle with continuous spin and its twistorial description, JHEP 1807 (2018) 031, [arXiv: 1805.09706 [hep-th]]

    Pith/arXiv arXiv 2018

  31. [31]

    Buchbinder, V.A

    I.L. Buchbinder, V.A. Krykhtin, H. Takata, BRST approach to Lagrangian construction for bosonic continuous spin field, Phys. Lett. B.785 (2018) 315, [arXiv:1806.01640[hep-th]]

    Pith/arXiv arXiv 2018

  32. [32]

    Buchbinder, S.A

    I.L. Buchbinder, S.A. Fedoruk, A.P. Isaev, V.A. Krykhtin, BRST construction for infinite spin field on AdS(4), Eur.Phys.J.Plus 139 (2024) 621, [arXiv:2403.14446[hep-th]]

    arXiv 2024

  33. [33]

    Buchbinder, S.A

    I.L. Buchbinder, S.A. Fedoruk, V.A. Krykhtin, Natural Sci.Rev. 2 (2025) 100301, [arXiv:2503.14290[hep-th]]

    arXiv 2025

  34. [34]

    Buchbinder, V.A

    I.L. Buchbinder, V.A. Krykhtin, L.L. Ryskina, BRST approach to Lagrangian formulation of bosonic totally antisymmeric tensor fields in curved space, Mod. Phys. Lett. A 24 (2009) 401, [arxiv:0810.3467[hep-th]]

    Pith/arXiv arXiv 2009

  35. [35]

    Buchbinder, V.A

    I.L. Buchbinder, V.A. Krykhtin, L.L. Ryskina, Lagrangian formulation of massive fermionic totally antisymmetric tensor field theory inAdS d space, Nucl. Phys. B 819 (2009) 453, [arxiv:0902.1471[hep-th]]

    Pith/arXiv arXiv 2009

  36. [36]

    Zinoviev, Note on antisymmetric spin-tensors, JHEP 04 (2009) 035, [arXiv:0903.0262[hep-th]]

    Yu.M. Zinoviev, Note on antisymmetric spin-tensors, JHEP 04 (2009) 035, [arXiv:0903.0262[hep-th]]

    Pith/arXiv arXiv 2009

  37. [37]

    de Medeiros and C

    P. de Medeiros and C. Hull, JHEP 0305 (2003) 019, [arxiv:hep-th/0303036]

    Pith/arXiv arXiv 2003

  38. [38]

    Alkalaev, Theor.Math.Phys

    K.B. Alkalaev, Theor.Math.Phys. 140 (2004) 1253, [arxiv:hep-th/0311212]

    Pith/arXiv arXiv 2004

  39. [39]

    Boulanger, S

    N. Boulanger, S. Cnockaert, Consistent deformations of [p,p]-type gauge field theories, JHEP 0403 (2004) 031, [arxiv:hep-th/0402180]. 35

    Pith/arXiv arXiv 2004

  40. [40]

    Bekaert, N

    X. Bekaert, N. Boulanger, S. Cnockaert, No Self-Interaction for Two-Column Massless Fields, J. Math. Phys. 46 (2005) 012303, [arxiv:hep-th/0407102]

    Pith/arXiv arXiv 2005

  41. [41]

    Yu. M. Zinoviev, Massive two-column bosonic fields in the frame-like formalism, Nucl.Phys.B913 (2016) 301, [arxiv:1607.08476[hep-th]]

    Pith/arXiv arXiv 2016

  42. [42]

    A. A. Reshetnyak, BRST-BFV Lagrangian formulations for Higher-Spin fields subject to two-column Young tableaux, TSPU Bulletin. 12 (2014) 211, [arXiv:1412.0200[hep-th]]

    Pith/arXiv arXiv 2014

  43. [43]

    A. A. Reshetnyak, Gauge-invariant Lagrangians for mixed-antisymmetric higher spin fields, Phys. Part. Nucl. Lett. 14 (2017) 371-375, [arXiv:1604.00620[hep-th]]

    Pith/arXiv arXiv 2017

  44. [44]

    Reshetnyak, Yu.V

    A.A. Reshetnyak, Yu.V. Bogdanova, V.K. Pandey, On Lagrangian formulations for (ir)reducible mixed-antisymmetric higher integer spin fields in Minkowski spaces, Moscow Univ. Phys.Bull. 80 (2025) S.2 S690-S700, [arXiv : 2509.09490[hep-th]]

    arXiv 2025

  45. [45]

    Becchi, A

    C. Becchi, A. Rouet, R. Stora, Renormalization Of The Abelian Higgs-Kibble Model, Comm. Math. Phys. 42 (1975) 127

    1975

  46. [46]

    Tyutin, Gauge invariance in field theory and ststistical mechanics

    I.V. Tyutin, Gauge invariance in field theory and ststistical mechanics. Lebedev Inst. preprint No. 39 (1975), [arXiv:0812.0580 [hep-th]]

    Pith/arXiv arXiv 1975

  47. [47]

    Faddeev, V.N

    L.D. Faddeev, V.N. Popov, Feynman Diagrams for the Yang-Mills Field, Phys.Lett. 25 (1967) 29

    1967

  48. [48]

    Fradkin, G.A

    E.S. Fradkin, G.A. Vilkovisky, Quantization of relativistic systems with constraints, Phys. Lett. B 55 (1975) 224

    1975

  49. [49]

    Batalin, G.A

    I.A. Batalin, G.A. Vilkovisky, RelativisticS-matrix of dynamical systems with boson and fermion constraints, Phys. Lett. B 69 (1977) 309

    1977

  50. [50]

    Batalin, E.S

    I.A. Batalin, E.S. Fradkin, A generalized canonical formalism and quantization of reducible gauge theories, Phys. Lett. B 128 (1983) 303

    1983

  51. [51]

    Alexandrov, M

    M. Alexandrov, M. Kontsevich, A. Schwarz, O. Zaboronsky, The geometry of the mas- ter equation and topological quantum field theory, Int. J. Mod. Phys. A. 12 (1997) 1405, [arXiv:hep-th /9502010]

    1997

  52. [52]

    Grigoriev, A

    M. Grigoriev, A. Kotov, Presymplectic AKSZ formulation of Einstein gravity, JHEP 05 (2022) 020, [arxiv:2106.07966 [hep-th]]

    arXiv 2022

  53. [53]

    Grigoriev, V

    M. Grigoriev, V. Gritzaenko, Massive bigravity as a presymplectic BV-AKSZ sigma-model, JHEP 01 (2025) 130, [arxiv:2410.13075[hep-th]]

    arXiv 2025

  54. [54]

    Dirac, Generalized Hamiltonian dynamics, Canadian J.of Mathematics 2 (1950) 129–148

    P.A.M. Dirac, Generalized Hamiltonian dynamics, Canadian J.of Mathematics 2 (1950) 129–148

    1950

  55. [55]

    Bergmann , I

    P. Bergmann , I. Goldberg, Dirac bracket transformations in phase space, Phys. Rev. 98 (1950) 531

    1950

  56. [56]

    A. A. Reshetnyak, Constrained BRST- BFV Lagrangian formulations for Higher Spin Fields in Minkowski Spaces, JHEP 09 (2018) 104, arXiv:1803.04678[hep-th]

    Pith/arXiv arXiv 2018

  57. [57]

    Bengtsson, Phys

    A.K.H. Bengtsson, Phys. Lett. B182 (1986) 321. 36

    1986

  58. [58]

    Barnich, M

    G. Barnich, M. Grigoriev, A. Semikhatov, I. Tipunin, Parent field theory and unfolding in BRST first-quantized terms, Comm. Math. Phys. 260 (2005) 147. [arXiv:hep-th/0406192]

    Pith/arXiv arXiv 2005

  59. [59]

    Pashnev, M

    A. Pashnev, M. Tsulaia, Description of the higher massless irreducible integer spins in the BRST approach, Mod. Phys. Lett. A13 (1998) 1853, [arXiv:hep-th/9803207]

    Pith/arXiv arXiv 1998

  60. [60]

    Burdik, A

    C. Burdik, A. Pashnev, M. Tsulaia, On the mixed symmetry irreducible representations of the Poincare group in the BRST approach, Mod. Phys. Lett. A16 (2001) 731, [arXiv:hep- th/0101201]

    arXiv 2001

  61. [61]

    Burdik, A

    C. Burdik, A. Pashnev, M. Tsulaia, The Lagrangian description of representations of the Poincare group, Nucl. Phys. Proc. Suppl. 102 (2001) 285, [arXiv:hep-th/0103143]

    Pith/arXiv arXiv 2001

  62. [62]

    Buchbinder, A

    I.L. Buchbinder, A. Pashnev, M. Tsulaia, Lagrangian formulation of the massless higher integer spin fields in the AdS background, Phys. Lett. B523 (2001) 338, [arXiv:hep- th/0109067]

    arXiv 2001

  63. [63]

    Faddeev, S.L

    L.D. Faddeev, S.L. Shatashvili, Realization of the Schwinger term in the Gauss low and the possibility of correct quantization of a theory with anomalies, Phys.Lett. B167 (1986) 225

    1986

  64. [64]

    Batalin, E.S

    I.A. Batalin, E.S. Fradkin, T.E. Fradkina, Another version for operatorial quantization of dynamical systems with iireducible constraints, Nucl. Phys. B314 (1989) 158–174

    1989

  65. [65]

    Batalin, I.V

    I.A. Batalin, I.V. Tyutin, Existence theorerm for the effective gauge algebra in the gener- alized canonical formalism and Abelian conversion of second class constraints, Int. J. Mod. Phys. A6 (1991) 3255

    1991

  66. [66]

    Egorian, R

    E. Egorian, R. Manvelyan, Quantization of dynamical systems with first and second class constraints, Theor. Math. Phys. 94 (1993) 241–252

    1993

  67. [67]

    Bekaert, I.L

    X. Bekaert, I.L. Buchbinder, A. Pashnev, M. Tsulaia, On higher spin theory: strings, BRST, dimensional reductions, Class. Quant. Grav. 21 (2004) 1457, [arXiv:hep-th/0312252]

    Pith/arXiv arXiv 2004

  68. [68]

    Buchbinder, V.A

    I.L. Buchbinder, V.A. Krykhtin, P.M. Lavrov, Gauge invariant Lagrangian formulation of higher massive bosonic field theory in AdS space, Nucl. Phys. B762 (2007) 344, [arXiv:hep- th/0608005]

    arXiv 2007

  69. [69]

    Buchbinder, V.A

    I.L. Buchbinder, V.A. Krykhtin, Gauge invariant Lagrangian construction for massive bosonic higher spin fields in D dimensions, Nucl. Phys. B727 (2005) 536, [arXiv:hep- th/0505092]

    arXiv 2005

  70. [70]

    Buchbinder, V.A

    I.L. Buchbinder, V.A. Krykhtin, A. Pashnev, BRST approach to Lagrangian construc- tion for fermionic massless higher spin fields, Nucl. Phys. B711 (2005) 367, [arXiv:hep- th/0410215]

    arXiv 2005

  71. [71]

    Buchbinder, V.A

    I.L. Buchbinder, V.A. Krykhtin, L.L. Ryskina, H. Takata, Gauge invariant Lagrangian con- struction for massive higher spin fermionic fields, Phys. Lett. B641 (2006) 386, [arXiv:hep- th/0603212]

    arXiv 2006

  72. [72]

    Buchbinder, V.A

    I.L. Buchbinder, V.A. Krykhtin, A.A. Reshetnyak, BRST approach to Lagrangian con- struction for fermionic higher spin fields in AdS space, Nucl. Phys. B787 (2007) 211, [arXiv:hep-th/0703049]. 37

    Pith/arXiv arXiv 2007

  73. [73]

    Buchbinder, V.A

    I.L. Buchbinder, V.A. Krykhtin, H. Takata, Gauge invariant Lagrangian construction for massive bosonic mixed-symmetry higher spin fields, Phys. Lett. B656 (2007) 253, [arXiv:0707.2181[hep-th]]

    Pith/arXiv arXiv 2007

  74. [74]

    Moshin, A.A

    P.Yu. Moshin, A.A. Reshetnyak, BRST Approach to Lagrangian Formulation for Mixed- Symmetry Fermionic Higher-Spin Fileds, JHEP 0710 (2007) 040, [arXiv:0706.0386[hep-th]]

    Pith/arXiv arXiv 2007

  75. [75]

    Buchbinder, V.A

    I.L. Buchbinder, V.A. Krykhtin, P.M. Lavrov, On manifolds admitting the consis- tent Lagrangian description for higher spin fields, Mod.Phys.Lett. A26 (2011) 1183, [arXiv:1101.4860[hep-th]]

    Pith/arXiv arXiv 2011

  76. [76]

    Buchbinder, A.A

    I.L. Buchbinder, A.A. Reshetnyak, General Cubic Interacting Vertex for Massless Integer Higher Spin Fields, Phys. Lett. B820 (2021) 136470, [arXiv:2105.12030 [hep-th]]

    arXiv 2021

  77. [77]

    Reshetnyak, Towards the structure of a cubic interaction vertex for massless integer higher spin fields, Phys

    A.A. Reshetnyak, Towards the structure of a cubic interaction vertex for massless integer higher spin fields, Phys. Part. Nucl. Lett. 19 (2022) 631, [arXiv:2205.00488 [hep-th]]

    arXiv 2022

  78. [78]

    Buchbinder, V.A

    I.L. Buchbinder, V.A. Krykhtin, T.V. Snegirev, Cubic interactions of d4 irreducible massless higher spin fields within BRST approach, Eur.Phys.J.C 82 (2022) 11, 1007, [arXiv:2208.04409 [hep-th]].)

    arXiv 2022

  79. [79]

    Buchbinder, A.A

    I.L. Buchbinder, A.A. Reshetnyak, Covariant Cubic Interacting Vertices for Massless and Massive Integer Higher Spin Fields, Symmetry 15 (2023) 2124; Correction, Symmetry 17 (2025) 145, [arXiv:2212.07097 [hep-th]]

    arXiv 2023

  80. [80]

    Buchbinder, A.A

    I.L. Buchbinder, A.A. Reshetnyak, Consistent Lagrangians for irreducible interact- ing higher-spin fields with holonomic constraints, Phys. Part. Nucl.54 (2023) 1066, [arXiv:2304.10358 [hep-th]]

    arXiv 2023

Showing first 80 references.