30 Citations (Scopus)

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 languageEnglish (US)
Pages (from-to)56-60
Number of pages5
JournalPhysics Letters B
Volume229
Issue number1-2
DOIs
StatePublished - Oct 5 1989

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gravitation
configurations
degrees of freedom

All Science Journal Classification (ASJC) codes

  • Nuclear and High Energy Physics

Cite this

Ashtekar, Abhay ; Romano, Joseph D. / Chern-Simons and palatini actions and (2+1)-gravity. In: Physics Letters B. 1989 ; Vol. 229, No. 1-2. pp. 56-60.
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Chern-Simons and palatini actions and (2+1)-gravity. / Ashtekar, Abhay; Romano, Joseph D.

In: Physics Letters B, Vol. 229, No. 1-2, 05.10.1989, p. 56-60.

Research output: Contribution to journalArticle

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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.

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