A calculus on Fock space and its probabilistic interpretations
نویسندگان
چکیده
منابع مشابه
A calculus on Fock space and its probabilistic interpretations
We introduce on the Fock space Γ(L(IR+)) two operators ∇ and ∇⊕ expressing the infinitesimal perturbations of random variables by time changes in the Wiener and Poisson probabilistic interpretations of Γ(L(IR+)). These operators have close connections with stochastic integration, regularity of laws, chaotic expansions and complement the annihilation and creation operators ∇− and ∇+ that are rel...
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A complete Fock space representation of the covariant differential calculus on quantum space is constructed. The consistency criteria for the ensuing algebraic structure, mapping to the canonical fermions and bosons and the consequences of the new algebra for the statistics of quanta are analyzed and discussed. The concept of statistical transmutation between bosons and fermions is introduced. ...
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These notes are intended as a fairly self contained explanation of Fock space and various algebras that act on it, including a Clifford algebras, a Weyl algebra, and an affine Kac-Moody algebra. We also discuss how the various algebras are related, and in particular describe the celebrated boson-fermion correspondence. We finish by briefly discussing a deformation of Fock space, which is a repr...
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ژورنال
عنوان ژورنال: Bulletin des Sciences Mathématiques
سال: 1999
ISSN: 0007-4497
DOI: 10.1016/s0007-4497(99)80016-5