Lorentz-covariant sampling theory for fields

Jason Pye

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

Abstract

Sampling theory is a discipline in communications engineering involved with the exact reconstruction of continuous signals from discrete sets of sample points. From a physics perspective, this is interesting in relation to the question of whether spacetime is continuous or discrete at the Planck scale, since in sampling theory we have functions which can be viewed as equivalently residing on a continuous or discrete space. Further, it is possible to formulate analogues of sampling which yield discreteness without disturbing underlying spacetime symmetries. In particular, there is a proposal for how this can be adapted for Minkowski spacetime. Here we will provide a detailed examination of the extension of sampling theory to this context. We will also discuss generally how spacetime symmetries manifest themselves in sampling theory, which at the surface seems in conflict with the fact that the discreteness of the sampling is not manifestly covariant. Specifically, we will show how the symmetry of a function space with a sampling property is equivalent to the existence of a family of possible sampling lattices related by the symmetry transformations.

Original languageEnglish
Article number025207
Number of pages26
JournalPhysica Scripta
Volume98
Issue number2
DOIs
Publication statusPublished - 1 Feb 2023

Fingerprint

Dive into the research topics of 'Lorentz-covariant sampling theory for fields'. Together they form a unique fingerprint.

Cite this