Journal
ANNALS OF PHYSICS
Volume 405, Issue -, Pages 92-100Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.aop.2019.03.014
Keywords
Quantum gravity phenomenology; Quantum gravity; Generalized uncertainty principle; Relativistic quantum mechanics; Dirac equation; Klein-Gordon equation
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Funding
- Natural Sciences and Engineering Research Council of Canada
- University of Lethbridge
- Universidad de Guanajuato
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The Generalized Uncertainty Principle and the related minimum length are normally considered in non-relativistic Quantum Mechanics. Extending it to relativistic theories is important for having a Lorentz invariant minimum length and for testing the modified Heisenberg principle at high energies. In this paper, we formulate a relativistic Generalized Uncertainty Principle. We then use this to write the modified Klein-Gordon, Schrodinger and Dirac equations, and compute quantum gravity corrections to the relativistic hydrogen atom, particle in a box, and the linear harmonic oscillator. (C) 2019 Elsevier Inc. All rights reserved.
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