Doubly special relativity as a non-local quantum field theory

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 (72)

• f(R) Theories Of Gravity
• Data Tables for Lorentz and CPT Violation
• Towards singularity and ghost free theories of gravity
• Quantum Spacetime Phenomenology
• Doubly Special Relativity
• Doubly Special Relativity theories as different bases of $\kappa$--Poincaré algebra
• Planck-scale modified dispersion relations and Finsler geometry
• A brief review of "little string theories"
• Riemann-Finsler geometry and Lorentz-violating kinematics
• Quadratic Gravity
• Deformed Field Theory on kappa-spacetime
• Mass-gap for black hole formation in higher derivative and ghost free gravity
• 2+1 gravity and Doubly Special Relativity
• Constraints and Stability in Vector Theories with Spontaneous Lorentz Violation
• Ghost-free infinite derivative quantum field theory
• String theory: a perspective over the last 25 years
• Field theory on $\kappa$--Minkowski space revisited: Noether charges and breaking of Lorentz symmetry
• Scalar Field Theory on Non-commutative Snyder Space-Time
• Hamilton geometry: Phase space geometry from modified dispersion relations
• Do massive compact objects without event horizon exist in infinite derivative gravity?
• Realization of DSR-relativistic symmetries in Finsler geometries
• The gravitational field of static p-branes in linearized ghost-free gravity
• Conformally-flat, non-singular static metric in infinite derivative gravity
• Electrodynamics on $\kappa$-Minkowski space-time
• Towards nonsingular rotating compact object in ghost-free infinite derivative gravity
• Generalized Causal Set d'Alembertians
• Tests of Quantum Gravity induced non-locality via opto-mechanical quantum oscillators
• Non-singular metric for an electrically charged point-source in ghost-free infinite derivative gravity
• Relativistic deformed kinematics from momentum space geometry
• Nonlocal star as a blackhole mimicker
• Lorentz invariance violation and charge (non--)conservation: A general theoretical frame for extensions of the Maxwell equations
• Scalar field theory on kappa-Minkowski spacetime and translation and Lorentz invariance
• Nonlocal Scalar Quantum Field Theory from Causal Sets
• Refringence, field theory, and normal modes
• Scalar field theory in Snyder space-time: alternatives
• Scalar field propagation in the phi^4 kappa-Minkowski model
• Effective delta sources and regularity in higher-derivative and ghost-free gravity
• Discrete Gravity Models and Loop Quantum Gravity: a Short Review
• Curved spacetimes with local $\kappa$-Poincaré dispersion relation
• Deformed relativity symmetries and the local structure of spacetime
• Planck-scale-modified dispersion relations in homogeneous and isotropic spacetimes
• Pauli-Jordan Function and Scalar Field Quantization in $\kappa$-Minkowski Noncommutative Spacetime
• Probing the quantum-gravity realm with slow atoms
• Phenomenological consequences of a geometry in the cotangent bundle
• Deformed relativistic kinematics on curved spacetime -- a geometric approach
• Aspects of a planar nonbirefringent and CPT-even electrodynamics stemming from the Standard Model Extension
• Generation of higher derivatives operators and electromagnetic wave propagation in a Lorentz-violation scenario
• Electrodynamics of a Generalized Charged Particle in Doubly Special Relativity Framework
• Quantum field theory in generalised Snyder spaces
• Causal Sets: Quantum gravity from a fundamentally discrete spacetime
• Worldline Formalism in Snyder Spaces
• Asymptotic freedom for $\lambda {\varphi }_{\star }^4$ QFT in Snyder-de Sitter space
• Nonassociative Snyder phi4 Quantum Field Theory
• $\kappa$-deformed complex fields and discrete symmetries
• Probing the vacuum fluctuations in scalar ghost-free theories
• String-Inspired Infinite-Derivative Theories of Gravity: A Brief Overview
• Geometrizing the Klein-Gordon and Dirac equations in Doubly Special Relativity
• Boson-boson effective nonrelativistic potential for higher-derivative electromagnetic theories in D dimensions
• Tests of Quantum Gravity-Induced Non-Locality via Opto-mechanical Experiments
• Status of Relativity with observer-independent length and velocity scales
• Renormalizability of nonlocal quantum gravity coupled to matter
• Lorentz invariance violation and electromagnetic field in an intrinsically anisotropic spacetime
• The Snyder-de Sitter Scalar ${\phi }_{\star }^4$ Quantum Field Theory in D=2
• Exponential Formulas and Lie Algebra Type Star Products
• Eikonal equation of the Lorentz-violating Maxwell theory
• Deformed Quantum Phase Spaces, Realizations, Star Products and Twists
• Classical electrodynamics on Snyder space
• Relativistic deformed kinematics: from flat to curved spacetimes
• Space-time thermodynamics in momentum dependent geometries
• Effective models of quantum gravity induced by Planck scale modifications in the covariant quantum algebra
• Higher-order theories from the minimal length
• Kappa-Minkowski differential calculi and star product

Cited by in corpus (3)

• Non-local quantum field theory from doubly special relativity
• On the Meaning of Localization in Non-Local Quantum Field Theory
• Relativistic electrodynamics with a universal length scale