Fock Space (2): Multiple Fock Spaces

Abstract

From the algebraic point of view, a multiple Fock space over ℌ is nothing but a standard (symmetric or antisymmetric) Fock space over a direct sum of copies of ℌ,and new definitions are not necessary in principle. However, this chapter contains important new notation, and a few rather interesting constructions, like that of the “finite-temperature” (= extremal universally invariant) representations of the CCR. In classical probability, it corresponds to the passage from one-dimensional to several-dimensional Brownian motion, necessary for Ito’s theory of stochastic differential equations.KeywordsBrownian MotionAnnihilation OperatorExchange OperatorTest VectorInitial SpaceThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.