Lorentz invariance with an invariant energy scale

Abstract

We propose a modification of special relativity in which a physical energy, which may be the Planck energy, joins the speed of light as an invariant, in spite of a complete relativity of inertial frames and agreement with Einstein's theory at low energies. This is accomplished by a non-linear modification of the action of the Lorentz group on momentum space, generated by adding a dilatation to each boost in such a way that the Planck energy remains invariant. The associated algebra has unmodified structure constants, and we highlight the similarities between the group action found and a transformation previously proposed by Fock. We also discuss the resulting modifications of field theory and suggest a modification of the equivalence principle which determines how the new theory is embedded in general relativity.

References in corpus (2)

• Quantum Gravity: a Progress Report
• Deformed Boost Transformations That Saturate at the Planck Scale

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• Complete density perturbations in the Jordan-Fierz-Brans-Dicke theory
• High energy neutrino oscillation at the presence of the Lorentz Invariance Violation
• On the Chandrasekhar Limit in Generalized Uncertainty Principles
• Nonlinear and Quantum Origin of Doubly Infinite Family of Modified Addition Laws for Fourmomenta
• Black hole complementarity with the generalized uncertainty principle in gravity's rainbow
• The Effects of Minimal Length in Entropic Force Approach
• Corrections to Scattering Processes due to Minimal Measurable Length
• Gravity waves in parity-violating Copernican Universes
• Classical and Quantum Dispersion Relations
• Special Relativity from Soft Gravitons
• The minimal length uncertainty and the nonextensive thermodynamics
• Quantum gravity phenomenology at the dawn of the multi-messenger era -- A review
• Discreteness of time in the evolution of the universe
• Reinterpreting deformed Heisenberg algebras
• Amelino-Camelia DSR effects on charged Dirac oscillators: Modulated spinning magnetic vortices
• The Phantom of the OPERA: Superluminal Neutrinos
• Once again about quantum deformations of D=4 Lorentz algebra: twistings of q-deformation
• Dirac neutrino mass from the beta decay end-point modified by the dynamics of a Lorentz-violating equation of motion
• Bounds on Relativistic Deformed Kinematics from the Physics of the Universe Transparency
• Electrostatic self-interaction of charged particles in the space-time of a cosmic string in the context of gravity's rainbow
• Comments on Nonlocality in Deformed Special Relativity, in reply to arXiv:1004.0664 by Lee Smolin and arXiv:1004.0575 by Jacob et al
• Quantum $\kappa$-Poincaré Algebra from de Sitter Space of Momenta
• Eikonal equation of the Lorentz-violating Maxwell theory
• Operational indistinguishably of varying speed of light theories
• Acceleration radiation and the Planck scale
• Time delay of light signals in an energy-dependent spacetime metric
• Photonic realization of the deformed Dirac equation via the segmented graphene nanoribbons under inhomogeneous strain
• The effect of modified dispersion relations on the thermodynamics of Schwarzschild black hole surrounded by quintessence
• GLAST and Lorentz violation
• A Projective Interpretation of Some Doubly Special Relativity Theories
• SIM$(1)$--VSR Maxwell-Chern-Simons electrodynamics
• Photon Gas at the Planck Scale within the Doubly Special Relativity
• Symmetries from Locality. II. Gravitation and Lorentz Boosts
• Corrections to flat-space particle dynamics arising from space granularity
• Lorentz violation with a universal minimum speed as foundation of de Sitter relativity
• Special relativity with two invariant scales: Motivation, Fermions, Bosons, Locality, and Critique
• Two-dimensional gravity with an invariant energy scale
• Intrinsic measurement errors for the speed of light in vacuum
• Accurate correction of arbitrary spin fermions quantum tunneling from non-stationary Kerr-de Sitter black hole based on corrected Lorentz dispersion relation
• Relativistic Bose-Einstein condensate in the rainbow gravity
• The more things change the more they stay the same: Minimum lengths with unmodified uncertainty principle and dispersion relation
• Constraints on Lorentz-invariance violation in the neutrino sector from the ultrahigh-energy event KM3-230213A
• A fundamental length as a candidate for dark energy: a DSR inspired FRW spacetime
• How can rainbow gravity affect on gravitational force?
• k-deformed Poincare algebras and quantum Clifford-Hopf algebras
• Time delays, choice of energy-momentum variables and relative locality in doubly special relativity
• Vacuum energy from noncommutative models
• Accelerated horizons and Planck-scale kinematics
• Asymptotic approach to Special Relativity compatible with a relativistic principle
• Universal entropy bound and discrete space-time
• 'Universal' FitzGerald Contractions
• Asymptotic quasinormal modes of scalar field in a gravity's rainbow
• De Sitter Special Relativity: Effects on Cosmology
• Emergent gravity: the BEC paradigm
• A Matter of Principle: The Principles of Quantum Theory, Dirac's Equation, and Quantum Information
• High-Energy gamma-ray Astronomy and String Theory
• A cosmological viewpoint on the correspondence between deformed phase-space and canonical quantization
• Invariant length scale in relativistic kinematics - Lessons from Dirichlet branes
• Quantum mechanics and geodesic deviation in the brane world
• Deformed Quantum Phase Spaces, Realizations, Star Products and Twists
• Challenging $\Lambda$CDM with Higher-Order GUP Corrections
• Quantum resolution of the cosmological singularity without new physics
• The Superluminal Neutrinos from Deformed Lorentz Invariance
• Dangerous implications of a minimum length in quantum gravity
• Hamiltonian formalism and spacetime symmetries in generic DSR models
• Noncommutative spaces and covariant formulation of statistical mechanics
• Group of boost and rotation transformations with two observer-independent scales
• Lorentz-violating dynamics in the pre-Planckian Universe
• Kappa-deformed Dirac oscillator in an external magnetic field
• Undeformed (additive) energy conservation law in Doubly Special Relativity
• Van der Waals Black Holes: Universality, Quantum Corrections, and Topological Classifications
• Massless Charged Particles Tunneling Radiation from a RN-dS Horizon and the Linear and Quadratic GUP
• Absorption cross section in gravity's rainbow from confluent Heun equation
• A spacetime realization of kappa-Poincare algebra
• Deformed Gazeau-Klauder Schrödinger-Cat States with Modified Commutation Relations
• Phenomenological Inclusion of Alternative Dispersion Relations to the Teukolsky Equation and its Application to Bounding the Graviton Mass with Gravitational-wave Measurements
• Impact of Cosmology on Lorentz Invariance Violation Constraints from GRB Time-Delays
• Testing Short Distance Anisotropy in Space
• Classical electrodynamics on Snyder space
• Semiclassical limit problems with concurrent use of several clocks in quantum cosmology
• Canonical, Lie-algebraic and quadratic twist deformations of Galilei group
• Squeezed atom laser for Bose-Einstein condensate with minimal length
• Lorentz Symmetry Breaking in $\mathcal{N}=2$ Superspace
• On the Klein-Gordon bosonic fields in the Bonnor-Melvin spacetime with a cosmological constant in rainbow gravity: Bonnor-Melvin Domain Walls
• Cosmic ray threshold in an asymptotically dS spacetime
• Squeezing the Parameter Space for Lorentz Violation in the Neutrino Sector by Additional Decay Channels
• Correlations between emission events in Rainbow Gravity
• Cosmological Model Independent Time Delay Method
• Lorentz Violation in Finsler Geometry
• Generalized relativistic kinematics in Poincaré-invariant models
• Lorentz breaking Effective Field Theory and observational tests
• Thermodynamics of black holes and the symmetric generalized uncertainty principle
• Black hole evaporation within a momentum-dependent metric
• The Abelian Higgs model and a minimal length in an un-particle scenario
• The cosmological implications of a fundamental length: a DSR inspired de-Sitter spacetime
• Backreaction mechanism in multifluid and extended cosmologies
• Lorentz violation with an invariant minimum speed as foundation of the uncertainty principle in Minkowski, dS and AdS spaces
• Unimodular Hartle-Hawking wave packets and their probability interpretation
• Symmetric ordering and Weyl realizations for quantum Minkowski spaces
• Quantum phase transitions of the Dirac oscillator in the Anti-Snyder model
• Deformed spaces and loop cosmology
• On the electrodynamics of moving particles in a quasi flat spacetime with Lorentz violation and its cosmological implications
• Note on uncertainty relations in doubly special relativity and rainbow gravity
• Non-Relativistic Anti-Snyder Model and Some Applications
• Two-body Dirac equation in DSR: results for fermion-antifermion pairs
• Rainbow Rindler metric and Unruh effect
• Particle-antiparticle asymmetry in a relativistic deformed kinematics
• Klein-Gordon oscillators in traversable wormhole rainbow gravity spacetime: Conditional exact solvability via a throat radius and oscillator frequency correlation
• $\kappa$-Minkowski and Snyder algebra from reparametrisation symmetry
• Symmetries from Locality. I. Electromagnetism and Charge Conservation
• Entropy spectrum of charged BTZ black holes in massive gravity's rainbow
• Fourth order deformed general relativity
• Causal loop in the theory of relative locality
• A covariant tapestry of linear GUP, metric-affine gravity, their Poincaré algebra and entropy bound
• Entropy bound for the photon gas in noncommutative spacetime
• Reappraisal of a model for deformed special relativity
• Maxwell's equations in the context of the Fock transformation and the magnetic monopole
• Top quark phenomenology of the ADD model and the Minimal Length Scenario
• Lorentz Violation of the Photon Sector in Field Theory Models
• Neutrinos and the Phenomenology of CPT Violation
• Multi-Dimensional Cosmology and DSR-GUP
• Virtual Black Holes from Generalized Uncertainty Principle and Proton Decay
• Two-dimensional gravity with an invariant energy scale and arbitrary dilaton potential
• Energy-momentum squared symmetric Teleparallel gravity: $f(Q,T_{\mu \nu }{T}^{\mu \nu })$ gravity
• Quantum Cosmology with Dynamical Vacuum in a Minimal-Length Scenario
• Free-fall Rainbow BTZ Black Hole
• Penetration of Arbitrary Double Potential Barriers with Probability Unity: Implications for Testing the Existence of a Minimum Length
• Momentum gauge fields from curved momentum space through Kaluza-Klein reduction
• Radial Oscillations and Dynamical Instability Analysis for Linear-Quadratic GUP-modified White Dwarfs
• Early universe thermostatistics in curved momentum spaces
• Notes on several phenomenological laws of quantum gravity
• Doubly Special Relativity with light-cone deformation
• Quantum Theory of Tensionless Noncommutative p-Branes
• Bigravity: a bimetric model of the Universe with variable constants, inluding VSL (variable speed of light)
• Linear-Quadratic GUP and Thermodynamic Dimensional Reduction
• Photon velocity, power spectrum in Unruh effect with modified dispersion relation
• Thermodynamics of a Schwarzschild black hole surrounded by quintessence in the generalized uncertainty principle framework
• Strong gravitational lensing by black hole in F(R) Euler Heisenberg Gravity's Rainbow
• Past and future blurring at fundamental length scale
• Energy-dependent topological anti-de Sitter black holes in Gauss-Bonnet Born-Infeld gravity
• Equilibrium properties of blackbody radiation with an ultraviolet energy cut-off
• Challenges Confronting Superluminal Neutrino Models
• Comment on arXiv:1007.0718 by Lee Smolin
• Remnants of black holes from rainbow gravity in terms of a new VSL theory
• New Chance for Researches on Lorentz Violation
• New perspective on space and time from Lorentz violation
• Fine-tuning problems in quantum field theory and Lorentz invariance: A scalar-fermion model with a physical momentum cutoff
• Effects of a Maximal Energy Scale in Thermodynamics for Photon Gas and Construction of Path Integral
• UV dimensional reduction to two from group valued momenta
• Trajectories of astroparticles in pseudo-Finsler spacetime with the most general modified dispersion
• A Field Theory Model With a New Lorentz-Invariant Energy Scale
• Exact form of Maxwell's equations and Dirac's magnetic monopole in Fock's nonlinear relativity
• Discreteness of Space from Anisotropic Spin-Orbit Interaction
• Quantum Noncanonical Field Theory: Symmetries and Interaction
• Black Holes Thermodynamics in a new kind of Noncommutative Geometry
• Signature Change by GUP
• Probing for Lorentz Invariance Violation in Pantheon Plus Dominated Cosmology
• Thermal properties of Klein-Gordon Oscillator in the Context of Amelino-Camelia and Magueijo-Smolin Doubly Special Relativity (DSR) frameworks
• Lorentz Symmetry and Ultra-High-Energy Cosmic Rays
• The Influence of Approximation in Generalized Uncertainty Principle on Black Hole Evaporation
• Symmetries from Locality. III. Massless Spin 2 Gravitons and Time Translations
• Dual Kappa Poincare Algebra
• Uncertainty of Velocity in kappa-Minkowski Spacetime
• Black hole dynamical evolution in a Lorentz-violating spacetime
• Planck scale effect on the thermodynamics of photon gas
• Five-Dimensional Mechanics as the Starting Point for the Magueijo-Smolin Doubly Special Relativity
• On the condensed matter scheme for emergent gravity and interferometry
• Klein-Gordon particles in a nonuniform external magnetic field in Bonnor-Melvin rainbow gravity background
• Deformations of the Schwarzschild Black Hole
• Propagation of spinors on a noncommutative spacetime: equivalence of the formal and the effective approach
• Loop Quantum Gravity Modification of the Compton Effect
• CPT analysis with top physics
• DSR and Canonical Transformations: A Comment on a ``A Lagrangian for DSR particle and the role of noncommutativity''
• Nucleosynthesis constraint on Lorentz invariance violation in the neutrino sector
• Immirzi Ambiguity, Boosts and Conformal Frames for Black Holes
• The noncommutative space of light-like worldlines
• New constraints on space-time Planck scale fluctuations from established high energy astronomy observations
• Ether and Relativity
• Muon accelerators -- Muon lifetime measurements as window to Planck scale physics
• The E(2) Particle
• Super-entropic black holes in gravity's rainbow and determining constraints on rainbow functions
• de Sitter relativity: a natural scenario for an evolving Lambda
• Lorentz violating electrodynamics
• Variation of the fundamental constants over the cosmological time: veracity of Dirac's intriguing hypothesis
• Probes for String-Inspired Foam, Lorentz, and CPT Violations in Astrophysics
• Cosmological constraints on Lorentz invariance violation in the neutrino sector
• A Special Lorentz Violation Model and a Special Rainbow Function
• Generalized Uncertainty Principle from the Regularized Self-Energy
• Unruh-Fulling effect in nonlocal field theory: The role of Unruh decomposition
• Non-minimal scalar-tensor theories
• Squeezing of light from Planck-scale physics
• Scalar field inflation driven by a modification of the Heisenberg algebra
• Quantum fate of timelike naked singularity with scalar hair
• Revisiting Varying Speed of Light in Cosmology: Insights from the Friedmann-Lemaître-Robertson-Walker Metric
• New Deformed Heisenberg Algebra from the $\mu$-Deformed Model of Dark Matter
• Lifetime of flying particles in canonical Doubly Special Relativity
• Relativistic Generalized Uncertainty Principle and Its Implications
• Effects of modified dispersion relations on free Fermi gas: equations of state and applications in astrophysics
• An Improved Framework for Quantum Gravity
• Special Relativity and its Newtonian Limit from a Group Theoretical Perspective
• Photon gas thermodynamics in dS and AdS momentum spaces
• Probing Fundamental Physics with Gravitational Waves
• Three dimensional DKP oscillator in a curved Snyder space
• Effects of Extended Uncertainty Principle on the Relativistic Coulomb Potential
• Bicrossproduct construction versus Weyl-Heisenberg algebra
• On massless and spinless particles with varying speed
• Conformal Generators and Doubly Special Relativity Theories
• Quantum Gravity Momentum Representation and Maximum Invariant Energy
• Another derivation of Weinberg's formula
• Nonlinear transforms of momenta and Planck scale limit
• Remarks on DSR and Gravity
• Classical gauge principle -- From field theories to classical mechanics
• Parameter estimation for a Lorentz invariance violation
• Removing the divergence of Chandrasekhar limit caused by generalized uncertainty principle
• From Fock's Transformation to de Sitter Space
• Relativity principle with a low energy invariant scale
• Could LIV/noncommutativity alleviate the cosmological constant problem
• Velocity and Distribution of Primordial Neutrinos
• Centripetal force on Casimir energies in $\kappa$-deformed rotating frame
• Large Extra Dimensions and the Minimal Length
• A mechanism to generate varying speed of light via Higgs-dilaton coupling: Theory and cosmological applications
• New analysis of SNeIa Pantheon Catalog: Variable speed of light as an alternative to dark energy
• Anti-de Sitter Momentum Space in 3D and 4D Quantum Gravity
• New Non-commutative and Higher Derivatives Quantum Mechanics from GUPs
• Lorentz-violating gaugeon formalism for rank-2 tensor theory
• Yang-Mills-Higgs models with higher order derivatives
• Conformal transformation route to gravity's rainbow
• Dirac's Equation in $R$-Minkowski Spacetime
• On Light-like Deformations of the Poincaré Algebra
• The Relativistic Particle and its d-brane Cousins
• Fuzzy Fluid Mechanics in Three Dimensions
• Variation of the light-like particle energy and its critical curve equations
• A Note on Coherent States with Quantum Gravity Effects
• Prospect of Chandrasekhar's limit against modified dispersion relation
• Some Features of Scattering Problem in a $\kappa$-Deformed Minkowski Spacetime
• Quantum Field Theory in fractal space-time with negative Hausdorff-Colombeau dimensions.The solution cosmological constant problem
• Quantum Spacetime Pictures and Dynamics from a Relativity Perspective
• Remarks on the interquark potential in the presence of a minimal length
• Lorentz-covariant sampling theory for fields
• 5-Dimensional $SO(1,4)$-Invariant Action as an Origin to the Magueijo-Smolin Doubly Special Relativity Proposal
• Electroweak symmetries from the topology of deformed spacetime with minimal length scale
• Noncommutative kappa-Minkowski phi4 theory: Construction, properties and propagation
• Modified Lorentz transformations in deformed special relativity
• Thermal effects of a photon gas with a deformed Heisenberg algebra
• LIV effects on the quantum stochastic motion in an acoustic FRW-geometry
• Maxwell's equations and Lorentz force in doubly special relativity
• Exact form of the generalized Lorentz force in Fock's nonlinear relativity
• From quantum deformations of relativistic symmetries to modified kinematics and dynamics
• Noncommutative scalar fields in compact spaces: quantisation and implications
• Non-singular Universes a la Palatini
• Time Evolution in Quantum Mechanics with a Minimal Time Scale
• Phonons mimicking doubly special relativity kinematics
• Ideal Quantum Gases with Planck Scale Limitations
• Quantum speed limit as a sensitive probe of Planck-scale effects
• Scaling-Based Quantization of Spacetime Microstructure
• Thermodynamic analysis of a compact object in Rastall-Rainbow gravity
• Quantum-Gravity phenomenology and high energy particle propagation
• On the Meaning of Localization in Non-Local Quantum Field Theory
• Massive Gauge Fields and the Planck Scale
• Quantum aether and an invariant Planck scale
• Homogeneous Spaces of the Lorentz Group
• A novel mechanism for probing the Planck scale with wavepackets following general distributions
• Gauge theory on kappa-Minkowski revisited: the twist approach
• Palatini approach to bouncing cosmologies and DSR-like effects
• Probing modified gravitational-wave dispersion with bursts from eccentric black-hole binaries
• Charged Massive Particle's Tunneling From Charged Non-Rotating Micro Black Hole
• Gamma Ray Bursts, The Principle of Relative Locality and Connection Normal Coordinates
• The Effect of Modified Dispersion Relation on Dumb Holes
• Comparison of the nonrelativistic limit of Amelino-Camelia and MS Doubly Special Relativity
• First considerations on the generalized uncertainty principle for finite-dimensional discrete phase spaces
• DSR-relativistic spacetime picture and the phenomenology of Planck-scale-modified time dilation
• Fuzzy worldlines with $\kappa$-Poincaré symmetries
• Modified Compton Effect and CMB Anisotropy
• Non-commutative correction of ideal gas thermodynamics
• The Varying Speed of Light in Eddington-inspired Born-Infield Gravity with Rainbow Metric
• Van der Waals black holes in rainbow gravity
• Twisting kappa-deformed phase space
• Statistical mechanics of ideal gas in the presence of minimal length and maximal momentum
• Lorentz Invariance Violation and Modified Hawking Fermions Tunneling from Black Strings
• Noncommutative (A)dS and Minkowski spacetimes from quantum Lorentz subgroups
• Aspects of Diffeomorphism Invariant Theory of Extended Objects I: The Relativistic Particle and its d-brane Cousins
• Quantum Gravity Corrections to the Mean Field Theory of Nucleons
• On the invariance of the relative rest in doubly special relativity
• Einstein-Yang-Mills Regular Black Holes in Rainbow Gravity
• Interaction of the generalized Duffin-Kemmer-Petiau equation with a non-minimal coupling under the cosmic rainbow gravity
• Three-dimensional gravity and deformations of relativistic symmetries
• A symplectic geometric origin of universal quartic modified dispersion relations
• The universe is not a Lie, but actually an Hopf, algebra
• GUP/BEB correspondence
• Phenomenological description of quantum gravity inspired modified classical electrodynamics
• Dimensional Phenomenology in Polymeric Quantization Framework
• Noncommutative effects in astrophysical objects: a survey
• Spontaneous Lorentz symmetry violation from infrared gravity
• Massive Neutron Stars and White Dwarfs as Noncommutative Fuzzy Spheres
• KG- oscillators in a spinning cosmic string spacetime and an external magnetic field
• Unruh effect using Doppler shift method in DSR framework
• Deformed Special Relativity using a Generalized 't Hooft-Nobbenhuis Complex Transformation
• Non Linear Lorentz Transformation and Doubly Special Relativity
• Analysis of black hole thermodynamics under Generalized uncertainty principle from the doubly special relativity
• The Accurate Modification of Tunneling Radiation of Fermions with Arbitrary Spin in Kerr-de Sitter Black Hole Space-time
• Decoherence limit of quantum systems obeying generalized uncertainty principle: new paradigm for Tsallis thermostatistics
• From the Schwarzschild Anti de Sitter Black Hole to the Conformal Field Theory
• Minimal-Length Corrections to Hyperon Polarization in Rotating Quark Gluon Plasma
• Towards an Entropic Geometrodynamics of Quantum Particles: Mouths of Casimir Wormholes as Planckeons
• A map between Galilean relativity and special relativity
• Five dimensional formulation of a DSR
• Snyder Like Modified Gravity in Newton's Spacetime
• Note About String Theory with Deformed Dispersion Relations
• Spacetime discreteness via consistent microscopic measurement
• Statistical physics on Euclidean Snyder space: connections with the GUP and cosmological implications
• Quantum fields in the non-perturbative regime - Yang-Mills theory and gravity
• Solutions of deformed three-dimensional gravity
• Doubly Special Relativity and quantum gravity phenomenology
• Extended Non Linear Conformal Symmetry and DSR Velocities on the Physical Surface
• Lorentz-breaking Theory and Tunneling Radiation Correction to Vaidya-Banner de Sitter Black Hole
• Can Light Signals Travel Faster than c in Nontrivial Vacuua in Flat space-time? Relativistic Causality II
• Relativistic electrodynamics with a universal length scale
• Super-Chandrasekhar limiting mass white dwarfs as emergent phenomena of noncommutative squashed fuzzy spheres
• Equations for fields with additional fundamental physical constants
• Primitively divergent diagrams in $\kappa$-deformed scalar field with quartic self-interaction
• Optical and Thermodynamic Signatures of Lorentz Symmetry Breaking in Bumblebee AdS Black Holes
• The effect of loop quantum gravitational rainbow functions on the formation of naked singularities
• Gravitational Redshift in Kerr-Newman Geometry Using Gravity's Rainbow
• A novel nonlocal spin-1/2 theory: classical and quantum aspects
• Extended 2d generalized dilaton gravity theories
• A winding number analysis of Schwarzschild black hole stability in light of Planck-scale modified kinematics
• Invariance of the fine structure constant with temperature of the expanding universe