Motivated by Segal’s axiom of conformal field theory, we do a survey on geometrical random fields. We do a history of continuous random fields in order to arrive at a field theoretical analog of Klauder’s quantization in Hamiltonian quantum mechanic by using infinite dimensional Airault-Malliavin Brownian motion.
"The geometry of Brownian surfaces." Probab. Surveys 3 37 - 88, 2006. https://doi.org/10.1214/154957806000000032