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.

References in corpus (5)

• Quadratic bosonic and free white noises
• The emergence of the Virasoro and $w_{\infty }$ algebras through the renormalized powers of quantum white noise
• Central extensions of the Heisenberg algebra
• Quantum white noise with singular non-linear interaction
• Squares of White Noise, SL(2,C) and Kubo - Martin -Schwinger States

Cited by in corpus (4)

• Scalar Field Quantization Without Divergences In All Spacetime Dimensions
• Quadratic exponential vectors
• A Poisson Algebra on the Hida Test Functions and a Quantization using the Cuntz Algebra
• Intertwinings for Continuum Particle Systems: an Algebraic Approach