Complex White Noise and Coherent State Representations

Nobuaki Obata

Takeyuki Hida

Luigi Accardi, Michael Skeide

The algebra of square of white noise1 contains a subalgebra generated by elements fulfilling the relations of Feinsilver's finite difference algebra.6 Moreover, Boukas' representation space3 is the same as the representation space of the algebra of square of white noise discovered in Ref. 2. In other words, Boukas' representation extends to a representation of the algebra of square of white noise.

Takeyuki Hida

Radhakrishnan Balu

We derive covariant Weyl operators for light-like fields, with the massless Weyl fermion as an illustrative example, in such a way that they correspond to quantum white noises in vacuum state of a symmetric Fock space.First, we build a representation of a light-like little group in terms of Weyl operators.We then use this construction to induce a representation of Poincaré group to construct relativistic quantum white noises from the fields via Mackey's systems of imprimitivity (SI) machinery.Our construction proceeds by fashioning the fermionic processes on a symmetric Fock space using reflection and identifying the corresponding processes on the isomorphic white noise space.