Covariant Quantum White Noise from Light-like Quantum Fields

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 Poincar\'e 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 re ection and identifying the corresponding processes on the isomorphic white noise space.