Relativistic Generalized Uncertainty Principle
Vasil Todorinov, Pasquale Bosso, Saurya Das
TL;DR
This paper develops a Lorentz-invariant relativistic Generalized Uncertainty Principle, modifies fundamental quantum equations accordingly, and calculates quantum gravity effects on key quantum systems.
Contribution
It introduces a relativistic formulation of the GUP, extending its applicability to high-energy physics and Lorentz-invariant quantum theories.
Findings
Modified Klein-Gordon, Schrödinger, and Dirac equations derived
Quantum gravity corrections computed for hydrogen atom, particle in a box, harmonic oscillator
Demonstrates the impact of GUP on relativistic quantum systems
Abstract
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, Schr\"odinger and Dirac equations, and compute quantum gravity corrections to the relativistic hydrogen atom, particle in a box, and the linear harmonic oscillator.
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