Quantum field theory with the generalized uncertainty principle I: scalar electrodynamics

Abstract

Recently, the authors presented a covariant extension of the Generalized Uncertainty Principle (GUP) with a Lorentz invariant minimum length. This opens the way for constructing and exploring the observable consequences of minimum length in Relativistic Quantum Field Theories. In particular, we compute quantum gravity corrections to high energy scattering experiments, which may provide the much needed window of testing minimum length and quantum gravity theories in the laboratory. To this end, we formulate the Lagrangian of Quantum Electrodynamics for a complex scalar fields from the GUP modified minimally coupled Klein-Gordon equation and write down its Feynman rules. We then calculate the Relativistic Generalized Uncertainty Principle corrections to a Quantum Electrodynamics scattering amplitude and discuss its implications.

Submitted to Annals o Physics

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• Massless polarized particle and Faraday rotation of light in the Schwarzschild spacetime
• Quantum gravitational signatures in next-generation gravitational wave detectors
• The solitary solutions of nonlinear Klein-Gordon field with minimal length
• The dominating mode of two competing massive modes of quadratic gravity
• Effect of RGUP on the nonlinear Klein-Gordon model with spontaneous symmetry breaking
• Minimal-length quantum field theory: a first-principle approach
• Relativistic Generalized Uncertainty Principle and Its Implications
• Generalized Uncertainty Principle: from the harmonic oscillator to a QFT toy model
• Finite Temperature Considerations in the Structure of Quadratic GUP-modified White Dwarfs
• UV Effects and Short-Lived Hawking Radiation: Alternative Resolution of Information Paradox
• Relativistic generalised uncertainty and the corrected vacuum energy