TY - JOUR
T1 - Self duality and quantization
AU - Ashtekar, Abhay
AU - Rovelli, Carlo
AU - Smolin, Lee
N1 - Funding Information:
We wish to thank Vince Moncrief for raising some of the issues discussed here and Ranjeet Tate and Lionel Mason for discussions on holomorphic distributions. This work was supported by the NSF grants INT88-15209, PHY90-12099 and PHY90-16733; by the research funds provided by Syracuse University; and by a SERC Senior Visiting Fellowship (to AA).
PY - 1992/3
Y1 - 1992/3
N2 - The quantum theory of the free Maxwell field in Minkowski space is constructed using a representation in which the self dual connection is diagonal. Quantum states are now holomorphic functionals of self dual connections and a decomposition of fields into positive and negative frequency parts is unnecessary. The construction requires the introduction of new mathematical techniques involving "holomorphic distributions". The method extends also to linear gravitons in Minkowski space. The fact that one can recover the entire Fock space - with particles of both helicities - from self dual connections alone provides independent support for a non-perturbative, canonical quantization program for full general relativity based on self dual variables.
AB - The quantum theory of the free Maxwell field in Minkowski space is constructed using a representation in which the self dual connection is diagonal. Quantum states are now holomorphic functionals of self dual connections and a decomposition of fields into positive and negative frequency parts is unnecessary. The construction requires the introduction of new mathematical techniques involving "holomorphic distributions". The method extends also to linear gravitons in Minkowski space. The fact that one can recover the entire Fock space - with particles of both helicities - from self dual connections alone provides independent support for a non-perturbative, canonical quantization program for full general relativity based on self dual variables.
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U2 - 10.1016/0393-0440(92)90041-X
DO - 10.1016/0393-0440(92)90041-X
M3 - Article
AN - SCOPUS:1642356223
SN - 0393-0440
VL - 8
SP - 7
EP - 27
JO - Journal of Geometry and Physics
JF - Journal of Geometry and Physics
IS - 1-4
ER -