Thermodynamics of ideal gas at Planck scale with strong quantum gravity measurement

Lawson, Latévi M.

doi:10.48550/arxiv.2103.00089

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Introduction1

Position-deformed Heisenberg Algebra1

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2021

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“…In this work [1], Perivolaropoulos also predicted the simultaneous existence of minimal and maximal length measurements More recently, one of us has shown that both measurable lengths can be obtained from position-dependent noncommutativity [6]. Its applications run from quantum optics [7], quantum thermodynamics [8] to non-Hermitian quantum mechanic scenarios [9].…”

Section: Introductionmentioning

confidence: 72%

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Hilbert space representation of maximal length and minimal momentum uncertainties

Amouzouvi¹,

Appiah²,

Lawson³

et al. 2021

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Perivolaropoulos has recently proposed a position-deformed Heisenberg algebra which includes a maximal length [Phys. Rev. D 95, 103523 (2017)]. He has shown that this length scale naturally emerges in the context of cosmological particle's horizon or cosmic topology. Following this work, we propose a new deformed algebra and derive the maximal length uncertainty and its corresponding minimal momentum uncertainty from the generalized uncertainty principle. We construct a Hilbert space representation in the spectral representation of this length scale. We also construct the corresponding Fourier transform and its inverse representations. Finally, we propose n-dimensional representation of this algebra.

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Section: Introductionmentioning

confidence: 72%

“…Let H τ = L 2 (R) be the Hilbert space of square integrable functions. D( X) and D( P ) are respectively the domains of operators X and P maximally dense in H. These operators X and P satisfy [6,7,8] […”

Section: Position-deformed Heisenberg Algebramentioning

confidence: 99%