Covariant Quantum White Noise from Light-like Quantum Fields

TL;DR

This paper develops covariant quantum white noise models for light-like quantum fields, exemplified by massless Weyl fermions, using group representations and Mackey's imprimitivity to connect fields with white noise processes.

Contribution

It introduces a covariant construction of quantum white noises for light-like fields, employing Weyl operators and Poincaré group representations, advancing the mathematical framework for relativistic quantum noise.

Findings

Constructed covariant Weyl operators for light-like fields.

Established a representation of the Poincaré group for quantum white noise.

Connected fermionic processes on Fock space with white noise models.

Abstract

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.