Regular Article - Theoretical Physics
Generalized uncertainty principle: from the harmonic oscillator to a QFT toy model
Theoretical Physics Group and Quantum Alberta, University of Lethbridge, 4401 University Drive, T1K 3M4, Lethbridge, AB, Canada
2 Dipartimento di Fisica, Università degli Studi di Salerno, Via Giovanni Paolo II, 132, 84084, Fisciano, SA, Italy
3 INFN, Sezione di Napoli, Gruppo collegato di Salerno, Via Giovanni Paolo II, 132, 84084, Fisciano, SA, Italy
Accepted: 31 October 2021
Published online: 9 November 2021
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.
© The Author(s) 2021
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