Quantum Probability, Renormalization and Infinite-Dimensional *-Lie Algebras

Abstract

The present paper reviews some intriguing connections which link together a new renormalization technique, the theory of *-representations of infinite dimensional *-Lie algebras, quantum probability, white noise and stochastic calculus and the theory of classical and quantum infinitely divisible processes.

Keywords

• quantum probability
• quantum white noise
• infinitely divisible process
• quantum decomposition
• Meixner classes
• renormalization
• infinite dimensional Lie algebra
• central extension of a Lie algebra