Minimal-length quantum field theory: a first-principle approach
arXiv:2407.13235 · doi:10.1140/epjc/s10052-024-13281-9
Abstract
Phenomenological models of quantum gravity often consider the existence of some form of minimal length. This feature is commonly described in the context of quantum mechanics and using the corresponding formalism and techniques. Although few attempts at a quantum field-theoretical description of a minimal length has been proposed, they are rather the exception and there is no general agreement on the correct one. Here, using the quantum-mechanical model as a guidance, we propose a first-principle definition of a quantum field theory including a minimal length. Specifically, we propose a two-step procedure, by first describing the quantum-mechanical models as a classical field theory and subsequently quantizing it. We are thus able to provide a foundation for further exploration of the implications of a minimal length in quantum field theory.
arXiv comment24 pages, 2 figures, 3 appendices
References in corpus (29)
- Hilbert Space Representation of the Minimal Length Uncertainty Relation
- Quantum gravity and minimum length
- A Generalized Uncertainty Principle in Quantum Gravity
- Generalized Uncertainty Principle in Quantum Gravity from Micro-Black Hole Gedanken Experiment
- Minimal Length Scale Scenarios for Quantum Gravity
- Quantum Spacetime Phenomenology
- Probing Planck-scale physics with quantum optics
- On Gravity and the Uncertainty Principle
- Quantum gravity, shadow states, and quantum mechanics
- Phenomenological Implications of the Generalized Uncertainty Principle
- Introduction to Doubly Special Relativity
- Minimum Length from Quantum Mechanics and Classical General Relativity
- Generalized Uncertainty Principle, Classical Mechanics, and General Relativity
- 30 years in: Quo vadis generalized uncertainty principle?
- Generalised uncertainty relations from superpositions of geometries
- Generalized uncertainty principles and quantum field theory
- Grin of the Cheshire cat: Entropy density of spacetime as a relic from quantum gravity
- Rigorous Hamiltonian and Lagrangian analysis of classical and quantum theories with minimal length
- Amplified transduction of Planck-scale effects using quantum optics
- Extended GUP formulation and the role of momentum cut-off
- On the quasi-position representation in theories with a minimal length
- Comparing two approaches to Hawking radiation of Schwarzschild-de Sitter black holes
- Quantum field theory with the generalized uncertainty principle I: scalar electrodynamics
- The minimal length: a cut-off in disguise?
- Doubly-Special Relativity: Facts, Myths and Some Key Open Issues
- Studies on the SJ Vacuum in de Sitter Spacetime
- Lorentz invariant mass and length scales
- Quantum metric for null separated events and spacetime atoms
- Why space could be quantised on a different scale to matter