The geometry of Brownian surfaces

Abstract

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.

Published at http://dx.doi.org/10.1214/154957806000000032 in the Probability Surveys (http://www.i-journals.org/ps/) by the Institute of Mathematical Statistics (http://www.imstat.org)

References in corpus (2)

• WZW branes and gerbes
• Heat Kernel Measure on Central Extension of Current Groups in any Dimension

Cited by in corpus (4)

• Two-parameter stochastic calculus and Malliavin's integration-by-parts formula on Wiener space
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• Hamiltonian stochastic Lie systems and applications
• Scaling limits of discrete copulas are bridged Brownian sheets