Self duality and quantization

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.