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 |
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All Science Journal Classification (ASJC) codes
- Nuclear and High Energy Physics
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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 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.
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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 -