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...
Enregistré dans:
| Auteurs principaux: | , |
|---|---|
| Format: | article |
| Langue: | EN |
| Publié: |
SpringerOpen
2021
|
| Sujets: | |
| Accès en ligne: | https://doaj.org/article/45aa0d41190846e2ab62d0a621154a72 |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| Résumé: | 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. |
|---|