pith. sign in

arxiv: 2606.24008 · v2 · 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 2026-07-01 06:28 UTC · model grok-4.3

classification ✦ hep-th math-phmath.DSmath.MPmath.RT
keywords higher-spin fieldsmixed-antisymmetric tensorsBRST formalismLagrangian formulationsPoincare representationsYoung tableauxVerma modulesHowe duality
0
0 comments X

The pith

Lagrangian formulations are constructed for higher-spin particles described by mixed-antisymmetric tensor fields with k-column Young tableaux in flat Minkowski space.

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

The paper establishes the first Lagrangian descriptions for both irreducible and reducible integer higher-spin massless and massive Poincare representations labeled by Young tableaux with k columns. The fields carry k groups of antisymmetric Lorentz indices and are treated in a metric-like setup through the BRST procedure. A key step converts the original system of operator constraints into first-class constraints by introducing auxiliary Fock modules from Verma representations that realize an so(k,k) algebra via Howe duality. This yields two equivalent gauge formulations, one unconstrained using the full BRST operator and one constrained using an incomplete operator plus algebraic conditions.

Core claim

The paper claims to present, for the first time, Lagrangian formulations for (ir)reducible integer higher-spin massless and massive Poincare group representations subject to Young tableau with k columns Y[ŝ1,ŝ2,...,ŝk] in d-dimensional Minkowski space-time. The particles are described by tensor fields with k groups of antisymmetric Lorentz indices via the BRST procedure with complete and incomplete BRST operators. The initial operator constraint system is converted into first-class constraints by realizing auxiliary representations of the constraint subalgebra through Verma modules isomorphic to so(k,k) via Howe duality, using new oscillator variables. Both unconstrained and constrained gaug

What carries the argument

Conversion of the initial second-class operator constraints on mixed-antisymmetric tensor fields into first-class constraints via auxiliary Verma-module representations of the constraint subalgebra, which are isomorphic to so(k,k) through Howe duality.

If this is right

  • Both an unconstrained formulation using the complete BRST operator Q and a constrained formulation using the incomplete operator Qc plus BRST-invariant algebraic constraints are obtained with equivalent dynamics.
  • The two formulations differ in their configuration spaces while describing the same physical content.
  • A notion of consistent interactions among these fields is outlined within the same BRST framework.

Where Pith is reading between the lines

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

  • The reliance on Howe duality for the auxiliary algebra suggests the method could extend to fields with mixed symmetry in other dimensions or with additional internal symmetries.
  • The separation into complete and incomplete BRST operators may allow systematic inclusion of interactions by deforming the BRST charge while preserving the first-class property.
  • Verification for low values of k would test whether the auxiliary Fock modules introduce no new physical states beyond those required by the Young tableau.

Load-bearing premise

The initial operator constraint system on the mixed-antisymmetric tensor fields can be converted into a system of first-class operator constraints by finding auxiliary representations of the constraint subalgebra via Verma modules that are isomorphic to so(k,k) through Howe duality.

What would settle it

Explicit computation of the equations of motion from the derived Lagrangian for the simplest case k=2 and spin s1=s2=2, checking whether they match the known massless or massive equations for a mixed-symmetry tensor without extraneous degrees of freedom.

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 manuscript claims to construct the first explicit 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 space. The fields are metric-like tensors with k groups of antisymmetric indices, treated via the BRST procedure with complete operator Q and incomplete operator Qc. The central technical step is conversion of the initial second-class operator constraints on an auxiliary Fock space (Poincaré module) into first-class constraints by adjoining auxiliary representations of the constraint subalgebra, realized via Verma modules that are isomorphic to so(k,k) through Howe duality and implemented with new oscillator variables.

Significance. If the algebraic constructions and equivalence of dynamics between the Q and Qc formulations hold, the result supplies a systematic BRST-based framework that unifies the treatment of mixed-antisymmetric higher-spin fields for arbitrary k, both massless and massive. This extends existing BRST methods beyond purely symmetric or antisymmetric cases and supplies a concrete route to gauge-invariant Lagrangians on flat space, which could serve as a starting point for interaction studies.

minor comments (2)
  1. Abstract: the phrases 'firstly presented' and 'in first time' are nonstandard; replace with 'presented for the first time'.
  2. Abstract: the sentence beginning 'To this aim, we find, in first time...' is grammatically awkward and should be rephrased for readability.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the positive summary and significance assessment of our manuscript on BRST formulations for mixed-antisymmetric higher-spin fields. The recommendation for minor revision is noted. No major comments were provided in the report, so we have no specific points requiring response or revision at this stage.

Circularity Check

0 steps flagged

No significant circularity identified

full rationale

The paper constructs Lagrangian formulations for higher-spin fields via BRST conversion of constraints, using Verma modules realizing so(k,k) via Howe duality. The abstract and procedure description contain no equations or steps that reduce by construction to fitted inputs, self-definitions, or load-bearing self-citations. The central claim is a direct technical extension of standard BRST methods with equivalent dynamics for Q and Qc operators; no reduction of results to inputs is exhibited. This is the expected self-contained case for a methods paper presenting explicit constructions.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 1 invented entities

Review performed on abstract only; several standard domain assumptions of higher-spin BRST theory are invoked but cannot be audited in detail.

axioms (2)
  • domain assumption Existence of an auxiliary Fock space associated with a special Poincare module for describing the mixed-antisymmetric fields
    Invoked at the start of the construction to realize the initial operator constraint system.
  • domain assumption Isomorphism via Howe duality between the constraint subalgebra and so(k,k) allowing auxiliary representations via Verma modules
    Used to convert second-class operators into first-class form with new oscillator variables.
invented entities (1)
  • new oscillator variables forming the Fock module no independent evidence
    purpose: to contain the subsystem of second-class operators after conversion
    Introduced to realize the conversion of the initial constraint system; no independent evidence supplied in abstract.

pith-pipeline@v0.9.1-grok · 5805 in / 1467 out tokens · 39672 ms · 2026-07-01T06:28:26.960867+00:00 · methodology

Review history (2 revisions) →

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

118 extracted references · 85 canonical work pages · 49 internal anchors

  1. [1]

    Higher Spin Gauge Theories in Various Dimensions

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

    work page internal anchor Pith review Pith/arXiv arXiv 2004

  2. [2]

    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]]

    work page internal anchor Pith review 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

    work page arXiv

  5. [5]

    Supersymmetry at BLTP: Recent Progress

    I.L. Buchbinder, E.A. Ivanov, Supersymmetry at BLTP: Recent Progress, Nat. Science Review 3 (2026) 200707, [arXiv:2606.25063[hep-th]]

    work page internal anchor Pith review Pith/arXiv arXiv 2026

  6. [6]

    Rep.175 (1989) 1

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

    1989

  7. [7]

    Witten, Noncommutative Geometry and String Field Theory, Nucl

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

    1986

  8. [8]

    Introduction to string field theory

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

    work page internal anchor Pith review Pith/arXiv arXiv 1988

  9. [9]

    On higher spins and the tensionless limit of String Theory

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

    work page internal anchor Pith review Pith/arXiv arXiv 2004

  10. [10]

    A Theory of Dark Matter

    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]]

    work page internal anchor Pith review Pith/arXiv arXiv 2009

  11. [11]

    How Dark Matter Came to Matter

    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]]

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  12. [12]

    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

  13. [13]

    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]]

    work page arXiv 2023

  14. [14]

    Gauge Invariant Lagrangians for Free and Interacting Higher Spin Fields. A Review of the BRST formulation

    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]]

    work page internal anchor Pith review Pith/arXiv arXiv 2009

  15. [15]

    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

  16. [16]

    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

  17. [17]

    Fronsdal, Massless Fields with Integer Spin, Phys

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

    1978

  18. [18]

    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

  19. [19]

    Minimal Local Lagrangians for Higher-Spin Geometry

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

    work page internal anchor Pith review Pith/arXiv arXiv 2005

  20. [20]

    Quartet unconstrained formulation for massive higher spin fields

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

    work page internal anchor Pith review Pith/arXiv arXiv 2008

  21. [21]

    Buchbinder, V.A

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

    work page arXiv 2007

  22. [22]

    Labastida, T.R

    J.M.F. Labastida, T.R. Morris, Massless mixed symmetry bosonic free fields, Phys. Lett. B180 (1986) 101. 34

    1986

  23. [23]

    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]

    work page internal anchor Pith review Pith/arXiv arXiv 2004

  24. [24]

    Alkalaev, O.V

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

    work page arXiv 2005

  25. [25]

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

    work page internal anchor Pith review Pith/arXiv arXiv 2009

  26. [26]

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

    work page internal anchor Pith review Pith/arXiv arXiv 2009

  27. [27]

    Unconstrained Higher Spins of Mixed Symmetry. I. Bose Fields

    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]]

    work page internal anchor Pith review Pith/arXiv arXiv 2009

  28. [28]

    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]]

    work page arXiv 2012

  29. [29]

    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]]

    work page arXiv 2013

  30. [30]

    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]]

    work page arXiv 2023

  31. [31]

    Model of massless relativistic particle with continuous spin and its twistorial description

    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]]

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  32. [32]

    BRST approach to Lagrangian construction for bosonic continuous spin field

    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]]

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  33. [33]

    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]]

    work page arXiv 2024

  34. [34]

    Buchbinder, S.A

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

    work page arXiv 2025

  35. [35]

    BRST approach to Lagrangian formulation of bosonic totally antisymmeric tensor fields in curved space

    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]]

    work page internal anchor Pith review Pith/arXiv arXiv 2009

  36. [36]

    Lagrangian formulation of massive fermionic totally antisymmetric tensor field theory in AdS_d space

    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]]

    work page internal anchor Pith review Pith/arXiv arXiv 2009

  37. [37]

    Note on antisymmetric spin-tensors

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

    work page internal anchor Pith review Pith/arXiv arXiv 2009

  38. [38]

    Geometric Second Order Field Equations for General Tensor Gauge Fields

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

    work page internal anchor Pith review Pith/arXiv arXiv 2003

  39. [39]

    Two-column higher spin massless fields in AdS(d)

    K.B. Alkalaev, Theor.Math.Phys. 140 (2004) 1253, [arxiv:hep-th/0311212]. 35

    work page internal anchor Pith review Pith/arXiv arXiv 2004

  40. [40]

    Consistent deformations of [p,p]-type gauge field theories

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

    work page internal anchor Pith review Pith/arXiv arXiv 2004

  41. [41]

    No Self-Interaction for Two-Column Massless Fields

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

    work page internal anchor Pith review Pith/arXiv arXiv 2005

  42. [42]

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

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  43. [43]

    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]]

    work page internal anchor Pith review Pith/arXiv arXiv 2014

  44. [44]

    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]]

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  45. [45]

    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]]

    work page arXiv 2025

  46. [46]

    Becchi, A

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

    1975

  47. [47]

    Gauge Invariance in Field Theory and Statistical Physics in Operator Formalism

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

    work page internal anchor Pith review Pith/arXiv arXiv 1975

  48. [48]

    Faddeev, V.N

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

    1967

  49. [49]

    Fradkin, G.A

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

    1975

  50. [50]

    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

  51. [51]

    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

  52. [52]

    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

  53. [53]

    Grigoriev, A

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

    work page arXiv 2022

  54. [54]

    Grigoriev, V

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

    work page arXiv 2025

  55. [55]

    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

  56. [56]

    Bergmann , I

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

    1950

  57. [57]

    A. A. Reshetnyak, Constrained BRST- BFV Lagrangian formulations for Higher Spin Fields in Minkowski Spaces, JHEP 09 (2018) 104, arXiv:1803.04678[hep-th]. 36

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  58. [58]

    Bengtsson, Phys

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

    1986

  59. [59]

    Parent field theory and unfolding in BRST first-quantized terms

    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]

    work page internal anchor Pith review Pith/arXiv arXiv 2005

  60. [60]

    Description of the higher massless irreducible integer spins in the BRST approach

    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]

    work page internal anchor Pith review Pith/arXiv arXiv 1998

  61. [61]

    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]

    work page arXiv 2001

  62. [62]

    The lagrangian description of representations of the Poincare group

    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]

    work page internal anchor Pith review Pith/arXiv arXiv 2001

  63. [63]

    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]

    work page arXiv 2001

  64. [64]

    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

  65. [65]

    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

  66. [66]

    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

  67. [67]

    Egorian, R

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

    1993

  68. [68]

    On Higher Spin Theory: Strings, BRST, Dimensional Reductions

    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]

    work page internal anchor Pith review Pith/arXiv arXiv 2004

  69. [69]

    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]

    work page arXiv 2007

  70. [70]

    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]

    work page arXiv 2005

  71. [71]

    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]

    work page arXiv 2005

  72. [72]

    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]. 37

    work page arXiv 2006

  73. [73]

    BRST approach to Lagrangian construction for fermionic higher spin fields in AdS space

    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]

    work page internal anchor Pith review Pith/arXiv arXiv 2007

  74. [74]

    Gauge invariant Lagrangian construction for massive bosonic mixed symmetry higher spin fields

    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]]

    work page internal anchor Pith review Pith/arXiv arXiv 2007

  75. [75]

    Contact 5-manifolds with SU(2)-structure

    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]]

    work page internal anchor Pith review Pith/arXiv arXiv 2007

  76. [76]

    On manifolds admitting the consistent Lagrangian formulation for higher spin fields

    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]]

    work page internal anchor Pith review Pith/arXiv arXiv 2011

  77. [77]

    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]]

    work page arXiv 2021

  78. [78]

    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]]

    work page arXiv 2022

  79. [79]

    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]].)

    work page arXiv 2022

  80. [80]

    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]]

    work page arXiv 2023

Showing first 80 references.