Infinite-dimensional extension of the spatiotemporal Kirkwood–Dirac framework

Extend the operator framework connecting Wightman correlators, spatiotemporal Kirkwood–Dirac quasiprobabilities, and spatiotemporal states from finite-dimensional systems to infinite-dimensional systems, particularly for applications to quantum field theory.

Background

The paper develops its principal constructions for finite-dimensional quantum systems, including recursive spatiotemporal states, Kirkwood–Dirac and Margenau–Hill quasiprobabilities, temporality measures, and entropy-based descriptions of spatiotemporal entanglement. A systematic treatment of infinite-dimensional systems is not provided within the paper.

The authors identify extending the framework to infinite-dimensional settings as an open direction, motivated especially by the need to apply these constructions to quantum field theory, where the underlying Hilbert spaces and observable algebras may be infinite-dimensional and require additional analytic control.