High Energy Physics - Theory · arXiv:1101.4860 v2 · submitted 25 Jan 2011
On manifolds admitting the consistent Lagrangian formulation for higher spin fields
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“This result finally proves that the consistent Lagrangian formulation at the conditions under consideration is possible only in constant curvature Riemann space.”
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The paper
Abstract
We study a possibility of Lagrangian formulation for free higher spin bosonic totally symmetric tensor field on the background manifold characterizing by the arbitrary metric, vector and third rank tensor fields in framework of BRST approach. Assuming existence of massless and flat limits in the Lagrangian and using the most general form of the operators of constraints we show that the algebra generated by these operators will be closed only for constant curvature space with no nontrivial coupling to the third rank tensor and the strength of the vector fields. This result finally proves that the consistent Lagrangian formulation at the conditions under consideration is possible only in constant curvature Riemann space.
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abstract compiled · 2026-09-23 · no language-model review
How the main claim is stated: asserted 1.00
What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.87 · human participants 0.01 · controlled comparison 0.03 · randomized assignment 0.01 · states quantitative result 0.06 · compares with prior results 0.08 · mentions code or data availability 0.01
The abstract, sentence by sentence
This table labels the abstract only (arXiv listing abstract v2). The number is the probability the classifier gave the label.
| Sentence | Role | The authors' own work | States the main conclusion | Strength |
|---|---|---|---|---|
| We study a possibility of Lagrangian formulation for free higher spin bosonic totally symmetric tensor field on the background manifold characterizing by the arbitrary metric, vector and third rank tensor fields in framework of BRST approach. | contribution 0.99 | 0.84 | 0.03 | hedged possibility 0.87 |
| Assuming existence of massless and flat limits in the Lagrangian and using the most general form of the operators of constraints we show that the algebra generated by these operators will be closed only for constant curvature space with no nontrivial coupling to the third rank tensor and the strength of the vector fields. | result 0.81 | 0.92 | 0.21 | asserted 1.00 |
| This result finally proves that the consistent Lagrangian formulation at the conditions under consideration is possible only in constant curvature Riemann space. | result 0.85 | 0.88 | 0.95 | asserted 1.00 |
What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 1.00
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Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,055 input tokens, $0.0001 reported.
Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. This record as JSON
Cited by 1 Pith paper
Reviewed papers on Pith that cite this one. The full citation record
How the literature uses it
5 arXiv papers cite this in 7 sentences
Papers citing it · 4 sentences without a confident label
Cites it as background 3 papers
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The BRST approach to Lagrangian formulation of higher spin field theories has been developed for arbitrary massless and massive, bosonic and fermionic fields in Minkowski and AdS spaces in [ref] – [ref] .
General Lagrangian Formulation for Higher Spin Fields with Arbitrary Index Symmetry. I. Bosonic fields · Introduction · 0.94
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In AdS space, the nonlinear bosonic subalgebra of operators has been studied in [ref] , while the full supersymmetric algebra was considered in [ref] .
The Involutive System of Higher-Spin Equations · Lie Algebra of Operators · 0.86
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We were also informed of related works [ref] [ref] [ref] [ref] [ref] [ref] [ref] [ref] [ref] [ref] [ref] [ref] [ref] [ref] [ref] .
Massive higher spin fields in curved spacetime and necessity of non-minimal couplings · Introduction · 0.94
What it cites · 2 sentences without a confident label
Uses the method or tool of 2 papers
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The proof is based on generic BRST formulation of higher spin field theory (see the various use of BRST formalism in higher spin field theory in [ref] which allows efficiently to study the bosonic and fermionic, massless and massive higher spin fields, to take into account a gauge structure of the theory and to work with tensor fields of various symmetry of indices.
Massless Higher Spin Fields in the AdS Background and BRST Constructions for Nonlinear Algebras · Introduction · 0.88
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The proof is based on generic BRST formulation of higher spin field theory (see the various use of BRST formalism in higher spin field theory in [ref] which allows efficiently to study the bosonic and fermionic, massless and massive higher spin fields, to take into account a gauge structure of the theory and to work with tensor fields of various symmetry of indices.
Off-shell Gauge Fields from BRST Quantization · Introduction · 0.88
Cites as background 3 papers
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Lagrangian formulation of interacting higher spin field theory is a fundamental unsolved problem of classical field theory during long time (see e.g. the reviews [ref] ).
An Introduction to Free Higher-Spin Fields · Introduction · 1.00
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Note that any third rank tensor can be decomposed into totally symmetric $S_(μνσ)$, totally antisymmetric $A_[μνσ]$ tensors, and tensors with mixed symmetry of the indices (see e.g. [ref] ).
The unitary representations of the Poincare group in any spacetime dimension · Introduction · 0.87
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Also, it would be interesting to study the consistency conditions for for recently formulated conformal higher spin fields [ref] if to couple them to external fields.
Ordinary-derivative formulation of conformal low-spin fields · Introduction · 0.85
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