Multi-Particle States in Deformed Special Relativity

Abstract

We investigate the properties of multi-particle states in Deformed Special Relativity (DSR). Starting from the Lagrangian formalism with an energy dependent metric, the conserved Noether current can be derived which is additive in the usual way. The integrated Noether current had previously been discarded as a conserved quantity, because it was correctly realized that it does no longer obey the DSR transformations. We identify the reason for this mismatch in the fact that DSR depends only on the extensive quantity of total four-momentum instead of the energy-momentum densities as would be appropriate for a field theory. We argue that the reason for the failure of DSR to reproduce the standard transformation behavior in the well established limits is due to the missing sensitivity to the volume inside which energy is accumulated. We show that the soccer-ball problem is absent if one formulates DSR instead for the field densities. As a consequence, estimates for predicted effects have to be corrected by many orders of magnitude. Further, we derive that the modified quantum field theory implies a locality bound.

replaced with published version

References in corpus (35)

• Hilbert Space Representation of the Minimal Length Uncertainty Relation
• Lorentz invariance with an invariant energy scale
• Relativity in space-times with short-distance structure governed by an observer-independent (Planckian) length scale
• Testable scenario for Relativity with minimum-length
• Generalized Lorentz invariance with an invariant energy scale
• Gravity's Rainbow
• The algebraic structure of the generalized uncertainty principle
• Quantum Groups, Gravity, and the Generalized Uncertainty Principle
• Planck-scale deformation of Lorentz symmetry as a solution to the UHECR and the TeV-$\gamma$ paradoxes
• Signatures in the Planck Regime
• TeV Astrophysics Constraints on Planck Scale Lorentz Violation
• New limits on Planck scale Lorentz violation in QED
• De Sitter space as an arena for Doubly Special Relativity
• Doubly Special Relativity and de Sitter space
• Interpretation of Quantum Field Theories with a Minimal Length Scale
• Self-consistency in Theories with a Minimal Length
• Non-Linear Relativity in Position Space
• Observational Limits on Quantum Geometry Effects
• Conservation Laws in Doubly Special Relativity
• Quantum-Gravity Phenomenology: Status and Prospects
• Falsifiable predictions from semiclassical quantum gravity
• Running Coupling with Minimal Length
• Loop Quantum Gravity and Ultra High Energy Cosmic Rays
• Possible astrophysical probes of quantum gravity
• Precursors, black holes, and a locality bound
• The information paradox and the locality bound
• A Lagrangian for DSR Particle and the Role of Noncommutativity
• Proposal of a second generation of quantum-gravity-motivated Lorentz-symmetry tests: sensitivity to effects suppressed quadratically by the Planck scale
• Interpreting doubly special relativity as a modified theory of measurement
• On reaction thresholds in doubly special relativity
• Could quantum gravity be tested with high intensity Lasers?
• Canonical DSR
• Some Consequences of a Generalization to Heisenberg Algebra in Quantum Electrodynamics
• On the Lorentz Transformations of Momentum and Energy
• Special relativity with two invariant scales: Motivation, Fermions, Bosons, Locality, and Critique

Cited by in corpus (46)

• Minimal Length Scale Scenarios for Quantum Gravity
• Quantum Spacetime Phenomenology
• Deformed Special Relativity and Deformed Symmetries in a Canonical Framework
• 30 years in: Quo vadis generalized uncertainty principle?
• Testing quantum gravity by nanodiamond interferometry with nitrogen-vacancy centers
• Relative locality and the soccer ball problem
• White Paper and Roadmap for Quantum Gravity Phenomenology in the Multi-Messenger Era
• A Note on Quantum Field Theories with a Minimal Length Scale
• Generalized Uncertainty Principle Removes The Chandrasekhar Limit
• Probing the quantum-gravity realm with slow atoms
• Thermodynamics of Photon Gas with an Invariant Energy Scale
• Palatini Actions and Quantum Gravity Phenomenology
• The Soccer-Ball Problem
• Snyder dynamics in a Schwarzschild spacetime
• Classical dynamics on curved Snyder space
• Relativistic Thermodynamics with an Invariant Energy Scale
• Inertial frames without the relativity principle
• Study of Lorentz violation in INTEGRAL Gamma-Ray Bursts
• Trapped Bose-Einstein condensates with Planck-scale induced deformation of the energy-momentum dispersion relation
• Doubly-Special Relativity: Facts, Myths and Some Key Open Issues
• Deformed Special Relativity from Asymptotically Safe Gravity
• Quantum-spacetime effects on nonrelativistic Schrödinger evolution
• Implications of minimum-length deformed quantum mechanics for QFT/QG
• Coherent states for generalized uncertainty relations as Tsallis probability amplitudes: new route to non-extensive thermostatistics
• Snyder Momentum Space in Relative Locality
• Covariant formulation of Generalised Uncertainty Principle
• Time delay of light signals in an energy-dependent spacetime metric
• Macroscopic body in Snyder space and minimal length estimation
• GLAST and Lorentz violation
• Dangerous implications of a minimum length in quantum gravity
• Minimum length, extra dimensions, modified gravity and black hole remnants
• A new perspective on Doubly Special Relativity
• Fourth order deformed general relativity
• Reappraisal of a model for deformed special relativity
• Equilibrium properties of blackbody radiation with an ultraviolet energy cut-off
• Effects of a Maximal Energy Scale in Thermodynamics for Photon Gas and Construction of Path Integral
• The general gravitational Lagrangian with deformed covariance
• Kinetic energy properties and weak equivalence principle in a space with GUP
• Weak equivalence principle and nonrelativistic limit of general dispersion relations
• Remarks on DSR and Gravity
• The general scalar-tensor Hamiltonian with deformed covariance
• Cosmic Neutrinos as a Window to Departures from Special Relativity
• Testing energy non-additivity in white dwarfs
• Deformed general relativity
• On the Meaning of Localization in Non-Local Quantum Field Theory
• Five dimensional formulation of a DSR