### Abstract

The general procedure for constructing a consistent covariant Dirac-type bracket for the models with mixed first and second class constraints is presented. The proposed scheme essentially relies upon explicit separation of the initial constraints into infinitely reducible first and second class ones (by making use of some covariant projectors). Reducibility of the second class constraints involved manifests itself in weakening some properties of the bracket as compared to the standard Dirac one. In particular, a commutation of any quantity with the second class constraints and the Jacobi identity holds on the second class constraints surface only. The procedure developed is realized for a N = 1 Brink-Schwarz superparticle in arbitrary dimension and for a N = 1, D = 9 massive superparticle with the Wess-Zumino term. The possibility to apply the bracket for quantizing the superparticles within the framework of the recent unified algebra approach by Batalin and Tyutin [20-22] is examined. It is shown, in particular, that for a D = 9 massive superparticle it is impossible to construct a Dirac-type bracket possessing a (strong) Jacobi identity in a full phase space.

Original language | English |
---|---|

Pages (from-to) | 245-266 |

Number of pages | 22 |

Journal | Nuclear Physics B |

Volume | 473 |

Issue number | 1-2 |

DOIs | |

Publication status | Published - 5 Aug 1996 |

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### ASJC Scopus subject areas

- Nuclear and High Energy Physics

### Cite this

*Nuclear Physics B*,

*473*(1-2), 245-266. https://doi.org/10.1016/0550-3213(96)00229-5

**Weak Dirac bracket construction and the superparticle covariant quantization problem.** / Deriglazov, A. A.; Galajinsky, A. V.; Lyakhovich, S. L.

Research output: Contribution to journal › Article

*Nuclear Physics B*, vol. 473, no. 1-2, pp. 245-266. https://doi.org/10.1016/0550-3213(96)00229-5

}

TY - JOUR

T1 - Weak Dirac bracket construction and the superparticle covariant quantization problem

AU - Deriglazov, A. A.

AU - Galajinsky, A. V.

AU - Lyakhovich, S. L.

PY - 1996/8/5

Y1 - 1996/8/5

N2 - The general procedure for constructing a consistent covariant Dirac-type bracket for the models with mixed first and second class constraints is presented. The proposed scheme essentially relies upon explicit separation of the initial constraints into infinitely reducible first and second class ones (by making use of some covariant projectors). Reducibility of the second class constraints involved manifests itself in weakening some properties of the bracket as compared to the standard Dirac one. In particular, a commutation of any quantity with the second class constraints and the Jacobi identity holds on the second class constraints surface only. The procedure developed is realized for a N = 1 Brink-Schwarz superparticle in arbitrary dimension and for a N = 1, D = 9 massive superparticle with the Wess-Zumino term. The possibility to apply the bracket for quantizing the superparticles within the framework of the recent unified algebra approach by Batalin and Tyutin [20-22] is examined. It is shown, in particular, that for a D = 9 massive superparticle it is impossible to construct a Dirac-type bracket possessing a (strong) Jacobi identity in a full phase space.

AB - The general procedure for constructing a consistent covariant Dirac-type bracket for the models with mixed first and second class constraints is presented. The proposed scheme essentially relies upon explicit separation of the initial constraints into infinitely reducible first and second class ones (by making use of some covariant projectors). Reducibility of the second class constraints involved manifests itself in weakening some properties of the bracket as compared to the standard Dirac one. In particular, a commutation of any quantity with the second class constraints and the Jacobi identity holds on the second class constraints surface only. The procedure developed is realized for a N = 1 Brink-Schwarz superparticle in arbitrary dimension and for a N = 1, D = 9 massive superparticle with the Wess-Zumino term. The possibility to apply the bracket for quantizing the superparticles within the framework of the recent unified algebra approach by Batalin and Tyutin [20-22] is examined. It is shown, in particular, that for a D = 9 massive superparticle it is impossible to construct a Dirac-type bracket possessing a (strong) Jacobi identity in a full phase space.

UR - http://www.scopus.com/inward/record.url?scp=0030570689&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0030570689&partnerID=8YFLogxK

U2 - 10.1016/0550-3213(96)00229-5

DO - 10.1016/0550-3213(96)00229-5

M3 - Article

AN - SCOPUS:0030570689

VL - 473

SP - 245

EP - 266

JO - Nuclear Physics B

JF - Nuclear Physics B

SN - 0550-3213

IS - 1-2

ER -