Stochastic evolution of Yang-Mills connections on the noncommutative two-torus

✍ Scribed by David Applebaum

• Publisher: Springer
• Year: 1988
• Tongue: English
• Weight: 288 KB
• Volume: 16
• Category: Article
• ISSN: 0377-9017
• DOI: 10.1007/bf00402015

✦ Synopsis

We study quantum stochastic parallel transport processes where the noise terms arise from quantum Brownian motion in Fock space and the connection is chosen to minimize the Yang-Mills functional on a Heisenberg module over the smooth algebra of the noncommutative two-torus. Each such process yields a dilation of a quantum dynamical semigroup whose action on components of the connection induces a family of transformations of the moduli space. From a physical point of view, this describes a highly singular interaction between quantized Yang-Mills fields and the free boson field.