Relativistic generalized uncertainty principle and its implications

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Todorinov, Vasil
University of Lethbridge. Faculty of Arts and Science
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Lethbridge, Alta. : University of Lethbridge, Dept. of Physics & Astronomy
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, Schrödinger and Dirac equations with QG corrections to several systems are presented. The Lagrangians of Quantum Electro-dynamics 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.
Dissertations, Academic , General relativity (Physics) , Heisenberg uncertainty principle , Quantum electrodynamics , Quantum gravity , Quantum theory , Relativistic quantum theory