  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.
