Generalized uncertainty principle: from the harmonic oscillator to a QFT toy model

Abstract Several models of quantum gravity predict the emergence of a minimal length at Planck scale. This is commonly taken into consideration by modifying the Heisenberg uncertainty principle into the generalized uncertainty principle. In this work, we study the implications of a polynomial genera...

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Auteurs principaux:	Pasquale Bosso, Giuseppe Gaetano Luciano
Format:	article
Langue:	EN
Publié:	SpringerOpen 2021
Sujets:	Astrophysics QB460-466 Nuclear and particle physics. Atomic energy. Radioactivity QC770-798
Accès en ligne:	https://doaj.org/article/45aa0d41190846e2ab62d0a621154a72
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id	oai:doaj.org-article:45aa0d41190846e2ab62d0a621154a72
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spelling	oai:doaj.org-article:45aa0d41190846e2ab62d0a621154a722021-11-14T12:13:55ZGeneralized uncertainty principle: from the harmonic oscillator to a QFT toy model10.1140/epjc/s10052-021-09795-11434-60441434-6052https://doaj.org/article/45aa0d41190846e2ab62d0a621154a722021-11-01T00:00:00Zhttps://doi.org/10.1140/epjc/s10052-021-09795-1https://doaj.org/toc/1434-6044https://doaj.org/toc/1434-6052Abstract Several models of quantum gravity predict the emergence of a minimal length at Planck scale. This is commonly taken into consideration by modifying the Heisenberg uncertainty principle into the generalized uncertainty principle. In this work, we study the implications of a polynomial generalized uncertainty principle on the harmonic oscillator. We revisit both the analytic and algebraic methods, deriving the exact form of the generalized Heisenberg algebra in terms of the new position and momentum operators. We show that the energy spectrum and eigenfunctions are affected in a non-trivial way. Furthermore, a new set of ladder operators is derived which factorize the Hamiltonian exactly. The above formalism is finally exploited to construct a quantum field theoretic toy model based on the generalized uncertainty principle.Pasquale BossoGiuseppe Gaetano LucianoSpringerOpenarticleAstrophysicsQB460-466Nuclear and particle physics. Atomic energy. RadioactivityQC770-798ENEuropean Physical Journal C: Particles and Fields, Vol 81, Iss 11, Pp 1-18 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Astrophysics QB460-466 Nuclear and particle physics. Atomic energy. Radioactivity QC770-798
spellingShingle	Astrophysics QB460-466 Nuclear and particle physics. Atomic energy. Radioactivity QC770-798 Pasquale Bosso Giuseppe Gaetano Luciano Generalized uncertainty principle: from the harmonic oscillator to a QFT toy model
description	Abstract Several models of quantum gravity predict the emergence of a minimal length at Planck scale. This is commonly taken into consideration by modifying the Heisenberg uncertainty principle into the generalized uncertainty principle. In this work, we study the implications of a polynomial generalized uncertainty principle on the harmonic oscillator. We revisit both the analytic and algebraic methods, deriving the exact form of the generalized Heisenberg algebra in terms of the new position and momentum operators. We show that the energy spectrum and eigenfunctions are affected in a non-trivial way. Furthermore, a new set of ladder operators is derived which factorize the Hamiltonian exactly. The above formalism is finally exploited to construct a quantum field theoretic toy model based on the generalized uncertainty principle.
format	article
author	Pasquale Bosso Giuseppe Gaetano Luciano
author_facet	Pasquale Bosso Giuseppe Gaetano Luciano
author_sort	Pasquale Bosso
title	Generalized uncertainty principle: from the harmonic oscillator to a QFT toy model
title_short	Generalized uncertainty principle: from the harmonic oscillator to a QFT toy model
title_full	Generalized uncertainty principle: from the harmonic oscillator to a QFT toy model
title_fullStr	Generalized uncertainty principle: from the harmonic oscillator to a QFT toy model
title_full_unstemmed	Generalized uncertainty principle: from the harmonic oscillator to a QFT toy model
title_sort	generalized uncertainty principle: from the harmonic oscillator to a qft toy model
publisher	SpringerOpen
publishDate	2021
url	https://doaj.org/article/45aa0d41190846e2ab62d0a621154a72
work_keys_str_mv	AT pasqualebosso generalizeduncertaintyprinciplefromtheharmonicoscillatortoaqfttoymodel AT giuseppegaetanoluciano generalizeduncertaintyprinciplefromtheharmonicoscillatortoaqfttoymodel
_version_	1718429342825971712

Generalized uncertainty principle: from the harmonic oscillator to a QFT toy model

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