Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)


SIGMA 5 (2009), 056, 31 pages      arXiv:0905.4491      http://dx.doi.org/10.3842/SIGMA.2009.056
Contribution to the Special Issue on Kac-Moody Algebras and Applications

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

Luigi Accardi a and Andreas Boukas b
a) Centro Vito Volterra, Università di Roma ''Tor Vergata'', Roma I-00133, Italy
b) Department of Mathematics, American College of Greece, Aghia Paraskevi, Athens 15342, Greece

Received November 20, 2008, in final form May 16, 2009; Published online May 27, 2009

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.

Key words: quantum probability; quantum white noise; infinitely divisible process; quantum decomposition; Meixner classes; renormalization; infinite dimensional Lie algebra; central extension of a Lie algebra.

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