High Energy Physics - Theory · arXiv:hep-th/0101089 v2 · submitted 14 Jan 2001
Star Product for Second Class Constraint Systems from a BRST Theory
The paper says
“We propose an explicit construction of the deformation quantization of the general second-class constrained system, which is covariant with respect to local coordinates on the phase space.”
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Abstract
We propose an explicit construction of the deformation quantization of the general second-class constrained system, which is covariant with respect to local coordinates on the phase space. The approach is based on constructing the effective first-class constraint (gauge) system equivalent to the original second-class one and can also be understood as a far-going generalization of the Fedosov quantization. The effective gauge system is quantized by the BFV-BRST procedure. The star product for the Dirac bracket is explicitly constructed as the quantum multiplication of BRST observables. We introduce and explicitly construct a Dirac bracket counterpart of the symplectic connection, called the Dirac connection. We identify a particular star product associated with the Dirac connection for which the constraints are in the center of the respective star-commutator algebra. It is shown that when reduced to the constraint surface, this star product is a Fedosov star product on the constraint surface considered as a symplectic manifold.
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abstract compiled · 2026-09-23 · no language-model review
How the main claim is stated: asserted 0.96
What the abstract itself states, as probabilities: claims first 0.06 · states limitation 0.06 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.02 · compares with prior results 0.73 · 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 propose an explicit construction of the deformation quantization of the general second-class constrained system, which is covariant with respect to local coordinates on the phase space. | contribution 1.00 | 0.95 | 0.54 | asserted 0.96 |
| The approach is based on constructing the effective first-class constraint (gauge) system equivalent to the original second-class one and can also be understood as a far-going generalization of the Fedosov quantization. | method 0.92 | 0.79 | 0.12 | asserted 0.91 |
| The effective gauge system is quantized by the BFV-BRST procedure. | method 0.99 | 0.69 | 0.05 | asserted 1.00 |
| The star product for the Dirac bracket is explicitly constructed as the quantum multiplication of BRST observables. | contribution 0.55 | 0.93 | 0.28 | asserted 1.00 |
| We introduce and explicitly construct a Dirac bracket counterpart of the symplectic connection, called the Dirac connection. | contribution 0.99 | 0.95 | 0.09 | asserted 1.00 |
| We identify a particular star product associated with the Dirac connection for which the constraints are in the center of the respective star-commutator algebra. | result 0.53 | 0.94 | 0.20 | asserted 1.00 |
| It is shown that when reduced to the constraint surface, this star product is a Fedosov star product on the constraint surface considered as a symplectic manifold. | result 0.92 | 0.90 | 0.26 | asserted 1.00 |
What kind of paper the classifier reports this is: method or tool 0.59 · evidence from proof or derivation 1.00
What was examined, and what was not
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- arXiv listing abstract v2
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- references and citing sentences
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- P abstract
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- S sections
- T body sentences
- C citations
- R cross-paper relations
How the labels were made
Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 5,556 input tokens, $0.0002 reported.
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Cited by 6 Pith papers
Reviewed papers on Pith that cite this one. The full citation record
- Parent field theory and unfolding in BRST first-quantized terms hep-th · Jun 2004
- Unified BRST approach to (partially) massless and massive AdS fields of arbitrary symmetry type hep-th · May 2011
- Unified BRST description of AdS gauge fields hep-th · Oct 2009
- Manifestly Conformal Descriptions and Higher Symmetries of Bosonic Singletons hep-th · Jul 2009
- Off-shell Gauge Fields from BRST Quantization hep-th · May 2006
- Parent form for higher spin fields on anti-de Sitter space hep-th · Feb 2006
How the literature uses it
3 arXiv papers cite this in 3 sentences
Papers citing it · 2 sentences without a confident label
Cites it as background 1 paper
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The identification of the Fedosov connection as a BRST operator was discussed in [ref] (see also [ref] ).
Massive Higher Spins from BRST and Tractors · Parent BRST Formulation of Tractor Fields · 0.82
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