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.
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