### Abstract

A path-integral quantization method is proposed for dynamical systems whose classical equations of motion do not necessarily follow from the action principle. The key new notion behind this quantization scheme is the Lagrange structure which is more general than the lagrangian formalism in the same sense as Poisson geometry is more general than the symplectic one. The Lagrange structure is shown to admit a natural BRST description which is used to construct an AKSZ-type topological sigma-model. The dynamics of this sigma-model in d+1 dimensions, being localized on the boundary, are proved to be equivalent to the original theory in d dimensions. As the topological sigma-model has a well defined action, it is path-integral quantized in the usual way that results in quantization of the original (not necessarily lagrangian) theory. When the original equations of motion come from the action principle, the standard BV path-integral is explicitly deduced from the proposed quantization scheme. The general quantization scheme is exemplified by several models including the ones whose classical dynamics are not variational.

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

Pages (from-to) | 1943-1984 |

Number of pages | 42 |

Journal | Journal of High Energy Physics |

Issue number | 7 |

DOIs | |

Publication status | Published - 1 Jul 2005 |

Externally published | Yes |

### Fingerprint

### Keywords

- BRST Quantization
- BRST Symmetry
- Gauge Symmetry

### ASJC Scopus subject areas

- Nuclear and High Energy Physics

### Cite this

*Journal of High Energy Physics*, (7), 1943-1984. https://doi.org/10.1088/1126-6708/2005/07/076

**Lagrange structure and quantization.** / Kazinski, Peter O.; Lyakhovich, Simon L.; Sharapov, Alexey A.

Research output: Contribution to journal › Article

*Journal of High Energy Physics*, no. 7, pp. 1943-1984. https://doi.org/10.1088/1126-6708/2005/07/076

}

TY - JOUR

T1 - Lagrange structure and quantization

AU - Kazinski, Peter O.

AU - Lyakhovich, Simon L.

AU - Sharapov, Alexey A.

PY - 2005/7/1

Y1 - 2005/7/1

N2 - A path-integral quantization method is proposed for dynamical systems whose classical equations of motion do not necessarily follow from the action principle. The key new notion behind this quantization scheme is the Lagrange structure which is more general than the lagrangian formalism in the same sense as Poisson geometry is more general than the symplectic one. The Lagrange structure is shown to admit a natural BRST description which is used to construct an AKSZ-type topological sigma-model. The dynamics of this sigma-model in d+1 dimensions, being localized on the boundary, are proved to be equivalent to the original theory in d dimensions. As the topological sigma-model has a well defined action, it is path-integral quantized in the usual way that results in quantization of the original (not necessarily lagrangian) theory. When the original equations of motion come from the action principle, the standard BV path-integral is explicitly deduced from the proposed quantization scheme. The general quantization scheme is exemplified by several models including the ones whose classical dynamics are not variational.

AB - A path-integral quantization method is proposed for dynamical systems whose classical equations of motion do not necessarily follow from the action principle. The key new notion behind this quantization scheme is the Lagrange structure which is more general than the lagrangian formalism in the same sense as Poisson geometry is more general than the symplectic one. The Lagrange structure is shown to admit a natural BRST description which is used to construct an AKSZ-type topological sigma-model. The dynamics of this sigma-model in d+1 dimensions, being localized on the boundary, are proved to be equivalent to the original theory in d dimensions. As the topological sigma-model has a well defined action, it is path-integral quantized in the usual way that results in quantization of the original (not necessarily lagrangian) theory. When the original equations of motion come from the action principle, the standard BV path-integral is explicitly deduced from the proposed quantization scheme. The general quantization scheme is exemplified by several models including the ones whose classical dynamics are not variational.

KW - BRST Quantization

KW - BRST Symmetry

KW - Gauge Symmetry

UR - http://www.scopus.com/inward/record.url?scp=23844511496&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=23844511496&partnerID=8YFLogxK

U2 - 10.1088/1126-6708/2005/07/076

DO - 10.1088/1126-6708/2005/07/076

M3 - Article

SP - 1943

EP - 1984

JO - Journal of High Energy Physics

JF - Journal of High Energy Physics

SN - 1126-6708

IS - 7

ER -