### Abstract

In this letter we make three observations: (i) Given any Lie group, G, the (2+1)-Palatini action is equivalent to the Chern-Simons action for an "inhomogenized" Lie group, IG, constructed from G. (ii) Since the reduced phase space of the Chern-Simons theory based on any group G is the reduced configuration space of the Palatini theory based on the same G - i.e., the Chern-Simons theory for IG-one can introduce additional structure on the configuration and phase-spaces of Palatini theories -including (2+1)-gravity-which plays an important role in their quantization. (iii) Using the first observation, one can couple Chern-Simons matter to (2+1)-gravity in a straightforward way. We point out that there is, however, a qualitative difference between this coupling and that of matter with genuine, local degrees of freedom.

Original language | English (US) |
---|---|

Pages (from-to) | 56-60 |

Number of pages | 5 |

Journal | Physics Letters B |

Volume | 229 |

Issue number | 1-2 |

DOIs | |

State | Published - Oct 5 1989 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Nuclear and High Energy Physics

### Cite this

*Physics Letters B*,

*229*(1-2), 56-60. https://doi.org/10.1016/0370-2693(89)90155-X

}

*Physics Letters B*, vol. 229, no. 1-2, pp. 56-60. https://doi.org/10.1016/0370-2693(89)90155-X

**Chern-Simons and palatini actions and (2+1)-gravity.** / Ashtekar, Abhay; Romano, Joseph D.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Chern-Simons and palatini actions and (2+1)-gravity

AU - Ashtekar, Abhay

AU - Romano, Joseph D.

PY - 1989/10/5

Y1 - 1989/10/5

N2 - In this letter we make three observations: (i) Given any Lie group, G, the (2+1)-Palatini action is equivalent to the Chern-Simons action for an "inhomogenized" Lie group, IG, constructed from G. (ii) Since the reduced phase space of the Chern-Simons theory based on any group G is the reduced configuration space of the Palatini theory based on the same G - i.e., the Chern-Simons theory for IG-one can introduce additional structure on the configuration and phase-spaces of Palatini theories -including (2+1)-gravity-which plays an important role in their quantization. (iii) Using the first observation, one can couple Chern-Simons matter to (2+1)-gravity in a straightforward way. We point out that there is, however, a qualitative difference between this coupling and that of matter with genuine, local degrees of freedom.

AB - In this letter we make three observations: (i) Given any Lie group, G, the (2+1)-Palatini action is equivalent to the Chern-Simons action for an "inhomogenized" Lie group, IG, constructed from G. (ii) Since the reduced phase space of the Chern-Simons theory based on any group G is the reduced configuration space of the Palatini theory based on the same G - i.e., the Chern-Simons theory for IG-one can introduce additional structure on the configuration and phase-spaces of Palatini theories -including (2+1)-gravity-which plays an important role in their quantization. (iii) Using the first observation, one can couple Chern-Simons matter to (2+1)-gravity in a straightforward way. We point out that there is, however, a qualitative difference between this coupling and that of matter with genuine, local degrees of freedom.

UR - http://www.scopus.com/inward/record.url?scp=0002339566&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0002339566&partnerID=8YFLogxK

U2 - 10.1016/0370-2693(89)90155-X

DO - 10.1016/0370-2693(89)90155-X

M3 - Article

VL - 229

SP - 56

EP - 60

JO - Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics

JF - Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics

SN - 0370-2693

IS - 1-2

ER -