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

• Main Authors: Luigi Accardi, Andreas Boukas
• Format: Article
• Language: English
• Published: National Academy of Science of Ukraine 2009-05-01
• Series: Symmetry, Integrability and Geometry: Methods and Applications
• Subjects: quantum probability; quantum white noise; infinitely divisible process; quantum decomposition; Meixner classes; renormalization; infinite dimensional Lie algebra; central extension of a Lie algebra
• Online Access: http://dx.doi.org/10.3842/SIGMA.2009.056

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.