Doubly special relativity as a non-local quantum field theory
arXiv:2403.19520 · doi:10.1103/PhysRevD.110.086004
Abstract
In this work, we explore the quantum theories of the free massive scalar, the massive fermionic, and the electromagnetic fields, in a doubly special relativity scenario. This construction is based on a geometrical interpretation of the kinematics of this kind of theory. In order to describe the modified actions, we find that a higher (indeed infinite) derivative field theory is needed, from which the deformed kinematics can be read. From our construction we are able to restrict the possible models of doubly special relativity to those that preserve linear Lorentz invariance. We quantize the theories and also obtain a deformed version of the Maxwell equations. We analyze the electromagnetic vector potential for both an electric pointlike source and magnetic dipole. We observe that the electric and magnetic fields do not diverge at the origin for some models described with an anti-de Sitter momentum space but do for the de Sitter one in both problems.
16 pages, 5 figures. Small improvements and added references in version 2
References in corpus (27)
- Planck-scale modified dispersion relations and Finsler geometry
- Riemann-Finsler geometry and Lorentz-violating kinematics
- Field theory on --Minkowski space revisited: Noether charges and breaking of Lorentz symmetry
- Do massive compact objects without event horizon exist in infinite derivative gravity?
- Realization of DSR-relativistic symmetries in Finsler geometries
- Generalized Causal Set d'Alembertians
- Nonlocal star as a blackhole mimicker
- Scalar field theory on kappa-Minkowski spacetime and translation and Lorentz invariance
- Nonlocal Scalar Quantum Field Theory from Causal Sets
- Scalar field theory in Snyder space-time: alternatives
- Discrete Gravity Models and Loop Quantum Gravity: a Short Review
- Planck-scale-modified dispersion relations in homogeneous and isotropic spacetimes
- Deformed relativity symmetries and the local structure of spacetime
- Deformed relativistic kinematics on curved spacetime -- a geometric approach
- Causal Sets: Quantum gravity from a fundamentally discrete spacetime
- Geometrizing the Klein-Gordon and Dirac equations in Doubly Special Relativity
- String-Inspired Infinite-Derivative Theories of Gravity: A Brief Overview
- Probing the vacuum fluctuations in scalar ghost-free theories
- Tests of Quantum Gravity-Induced Non-Locality via Opto-mechanical Experiments
- Renormalizability of nonlocal quantum gravity coupled to matter
- Lorentz invariance violation and electromagnetic field in an intrinsically anisotropic spacetime
- The Snyder-de Sitter Scalar Quantum Field Theory in D=2
- Eikonal equation of the Lorentz-violating Maxwell theory
- Deformed Quantum Phase Spaces, Realizations, Star Products and Twists
- Classical electrodynamics on Snyder space
- Space-time thermodynamics in momentum dependent geometries
- Relativistic deformed kinematics: from flat to curved spacetimes