Paul Jones (Loughborough) - "Implementors of Bogolubov transformations as solutions of quantum stochastic differential equations"

Abstract

Quantum stochastic calculus is a non-commutative extension of the Ito calculus of Brownian motion. Here we discuss some quantum stochastic differential equations, and show that their solution are unitary operators, conjugations by which implement Bogolubov transformations, which are automorphisms of the algebra of the canonical commutation relation underlying the quantum theory of systems of infinitely many degrees of freedom.