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

TL;DR

This paper explores the connections between quantum probability, renormalization techniques, and the mathematical structure of infinite-dimensional *-Lie algebras, highlighting their relevance to stochastic calculus and infinitely divisible processes.

Contribution

It reviews the interplay between renormalization, *-representations of infinite-dimensional *-Lie algebras, and quantum probability, proposing new links among these areas.

Findings

Identifies connections between renormalization and *-Lie algebra representations

Links quantum probability with infinite-dimensional algebraic structures

Highlights applications to stochastic calculus and infinitely divisible processes

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.