Modified commutators vs. modified operators in a quantum gravity minimal length scale

Bishop, Michael; Contreras, Joey; Lee, J.; Singleton, Douglas

doi:10.1063/5.0033527

Cited by 2 publications

(1 citation statement)

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“…Recently there have been proposals in the GUP literature about how one can obtain a finite minimum ΔX by modifying the position and momentum operators in a way that retains the canonical commutation relations [101][102][103][104] (see also [105]). One example from [101][102][103][104] is to define (in slightly different notation),…”

Section: Connection With Generalized Uncertainty Principlesmentioning

confidence: 99%

Lorentz-covariant sampling theory for fields

Pye

2023

Phys. Scr.

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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.

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