TY - JOUR

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

AU - Ashtekar, Abhay

AU - Romano, Joseph D.

N1 - Funding Information:
We would like to thank Ranjeet Tate for discussions. This research was supported in part by the NSF grants PHY86-12424 and INT88-15209 and by research funds provided by Syracuse University.

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

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

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

M3 - Article

AN - SCOPUS:0002339566

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 -