Relativistic Generalized Uncertainty Principle and Its Implications
arXiv:2108.04322
Abstract
The fundamental physical description of the Universe is based on two theories: Quantum Mechanics and General Relativity. Unified theory of Quantum Gravity (QG) is an open problem. Quantum Gravity Phenomenology (QGP) studies QG effects in low-energy systems. The basis of one such phenomenological model is the Generalized Uncertainty Principle (GUP), which is a modified Heisenberg uncertainty relation and predicts a deformed position-momentum commutator. Relativistic Generalized Uncertainty Principle (RGUP) is proposed in this thesis, which gives a Loerentz invariant minimum length and resolves the composition law problem. RGUP modified Klein-Gordon, Schrodinger and Dirac equations with QG corrections to several systems are presented. The Lagrangians of Quantum Electrodynamics for the gauge, scalar, and spinor fields are obtained. The RGUP corrections to scattering amplitudes are then calculated. The results are applied to high energy scattering experiments providing much needed window for testing minimum length and QG theories in the laboratory.
References in corpus (9)
- Universality of Quantum Gravity Corrections
- Prospects for constraining quantum gravity dispersion with near term observations
- Interpretation of Quantum Field Theories with a Minimal Length Scale
- The length operator in Loop Quantum Gravity
- Lorentz-covariant deformed algebra with minimal length
- New length operator for loop quantum gravity
- Conformal Invariance in noncommutative geometry and mutually interacting Snyder Particles
- Indeterminacy of Holographic Quantum Geometry
- Topological Defects in a Deformed Gauge Theory