Generalized Uncertainty Principle: from the harmonic oscillator to a QFT toy model

• URL: http://arxiv.org/abs/2109.15259v1
• Date: Thu, 30 Sep 2021 16:55:48 GMT
• Title: Generalized Uncertainty Principle: from the harmonic oscillator to a QFT toy model
• Authors: Pasquale Bosso and Giuseppe Gaetano Luciano
• Abstract summary: We modify the Heisenberg Uncertainty Principle into the Generalized Uncertainty Principle. We show that the energy spectrum and eigenfunctions are affected in a non-trivial way. We construct a quantum field theoretic toy model based on the Generalized Uncertainty Principle.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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