Stopping the CCR flow and its isometric cocycles

Belton, Alexander C. R. and Sinha, Kalyan B. (2014) Stopping the CCR flow and its isometric cocycles. The Quarterly Journal of Mathematics, 65 (4). pp. 1145-1164. ISSN 0033-5606

Abstract

It is shown how to use non-commutative stopping times in order to stop the CCR flow of arbitrary index and also its isometric cocycles, i.e. left operator Markovian cocycles on Boson Fock space. Stopping the CCR flow yields a homomorphism from the semigroup of stopping times, equipped with the convolution product, into the semigroup of unital endomorphisms of the von Neumann algebra of bounded operators on the ambient Fock space. The operators produced by stopping cocycles themselves satisfy a cocycle relation.