Self Duality and Quantization

Details Self Duality and Quantization Self Duality and Quantization

1992-02-24

arxiv.org/abs/hep-th/9202079v1

J.Geom.Phys.8:7-27,1992

Physics

High Energy Physics

High Energy Physics - Theory

14 pages

Scientific paper

10.1016/0393-0440(92)90041-X

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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