Fock Space (1)

Abstract

The preceding chapters dealt with the non-commutative analogues of discrete r.v.’s, then of real valued r.v.’s, and we now begin to discuss stochastic processes. We start with the description of Fock space (symmetric and antisymmetric) as it is usually given in physics books. Then we show that boson Fock space is isomorphic to the L ² space of Wiener measure, and interpret on Wiener space the creation, annihilation and number operators. We proceed with the Poisson interpretation of Fock space, and the operator interpretation of the Poisson multiplication. We conclude with multiplication formulas, and the useful analogy with “toy Fock space” in chapter II, which leads to the antisymmetric (Clifford) multiplications. All these operations are special cases of Maassen’s kernel calculus (§4).