A Note on Coherent State Representations of White Noise Operators

Nobuaki Obata

Abdessatar Barhoumi, Bilel Kacem Ben Ammou, Hafedh M. S. Rguigui

Sami H. Altoum, Hakeem A. Othman, Hafedh M. S. Rguigui

Aymen Ettaieb, Habib Ouerdiane, Hafedh M. S. Rguigui

In this paper we give the integral representation of the power of the quantum white noise (QWN) Euler operator (∆ Q E ) ρ , for ρ ∈ N, in terms of the QWN-derivatives {D - t , D + t ; t ∈ R} as a kind of functional integral acting on nuclear algebra of white noise operators.The solution of the Cauchy problem associated to (∆ Q E ) ρ is worked out in the basis of the QWN coordinate system.

Michel V. Romerio

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.