Space/Time Non-Commutativity and Causality

Abstract

Field theories based on non-commutative spacetimes exhibit very distinctive nonlocal effects which mix the ultraviolet with the infrared in bizarre ways. In particular if the time coordinate is involved in the non-commutativity the theory seems to be seriously acausal and inconsistent with conventional Hamiltonian evolution. To illustrate these effects we study the scattering of wave packets in a field theory with space/time non-commutativity. In this theory we find effects which seem to precede their causes and rigid rods which grow instead of Lorentz contract as they are boosted. These field theories are evidently inconsistent and violate causality and unitarity. On the other hand open string theory in a background electric field is expected to exhibit space/time non-commutativity. This raises the question of whether they also lead to acausal behavior. We show that this is not the case. Stringy effects conspire to cancel the acausal effects that are present for the non-commutative field theory.

New version replacing previous incorrect version

References in corpus (2)

• Space-Time Noncommutative Field Theories And Unitarity
• String Theory and the Space-Time Uncertainty Principle

Cited by in corpus (222)

• Noncommutative Field Theory
• Quantum Field Theory on Noncommutative Spaces
• Horizon-scale tests of gravity theories and fundamental physics from the Event Horizon Telescope image of Sagittarius A${}^{\ast }$
• On a Lorentz-Invariant Interpretation of Noncommutative Space-Time and Its Implications on Noncommutative QFT
• Non-Relativistic Closed String Theory
• Solving the Simplest Theory of Quantum Gravity
• New concept of relativistic invariance in NC space-time: twisted Poincaré symmetry and its implications
• Signals for Non-Commutative Interactions at Linear Colliders
• Noncommutative Standard Model: Model Building
• Coproduct and star product in field theories on Lie-algebra non-commutative space-times
• Derivation of a Vacuum Refractive Index in a Stringy Space-Time Foam Model
• On Theories With Light-Like Noncommutativity
• OM Theory in Diverse Dimensions
• Quantum Theories on Noncommutative Spaces with Nontrivial Topology: Aharonov-Bohm and Casimir Effects
• Dipoles, Twists and Noncommutative Gauge Theory
• Noncommutative Inspired Black Holes in Extra Dimensions
• Noncommutative ${\Phi }^4$ Theory at Two Loops
• Decay of Unstable D-branes with Electric Field
• Cosmological perturbations and short distance physics from Noncommutative Geometry
• Noncommutative QED and Anomalous Dipole Moments
• Spin-Statistics and CPT Theorems in Noncommutative Field Theory
• Natural Tuning: Towards A Proof of Concept
• Noncommutative Gravity
• On "full" twisted Poincare' symmetry and QFT on Moyal-Weyl spaces
• Hamiltonian Formalism for Space-time Non-commutative Theories
• Noncommutative Gauge Field Theories: A No-Go Theorem
• Noncommutative Quantum Mechanics: The Two-Dimensional Central Field
• Supergravity and Space-Time Non-Commutative Open String Theory
• A comparative review of four formulations of noncommutative quantum mechanics
• Time-ordered Perturbation Theory on Noncommutative Spacetime II: Unitarity
• Aspects of Nonrelativistic Strings
• Time Delays of Strings in D-particle Backgrounds and Vacuum Refractive Indices
• Duality and Non-Commutative Gauge Theory
• Fractional Hamiltonian analysis of higher order derivatives systems
• Chern-Simons action in noncommutative space
• Improved Z -> gamma gamma decay in the renormalizable gauge sector of the noncommutative standard model
• Perturbative Approach to Higher Derivative and Nonlocal Theories
• Implications of a Stochastic Microscopic Finsler Cosmology
• Phase diagram and dispersion relation of the non-commutative λϕ^{4} model in d=3
• Open Branes in Space-Time Non-Commutative Little String Theory
• A non-perturbative study of 4d U(1) non-commutative gauge theory -- the fate of one-loop instability
• Noncommutative Gravity in two Dimensions
• Stringy Space-Time Foam, Finsler-like Metrics and Dark Matter Relics
• Non-Commutativity and Unitarity Violation in Gauge Boson Scattering
• Integrable Noncommutative Sine-Gordon Model
• Perturbative Noncommutative Quantum Gravity
• Twist and Spin-Statistics Relation in Noncommutative Quantum Field Theory
• Phenomenology of Particle Production and Propagation in String-Motivated Canonical Noncommutative Spacetime
• Time-Space Noncommutativity in Gravitational Quantum Well scenario
• Supergravity Duals of Noncommutative Wrapped D6 Branes and Supersymmetry without Supersymmetry
• Noncommutative Scalar Quasinormal Modes of the Reissner Nordström Black Hole
• Pair Production by a Constant External Field in Noncommutative QED
• Noncommutative Lorentz Symmetry and the Origin of the Seiberg-Witten Map
• Towards an Axiomatic Formulation of Noncommutative Quantum Field Theory
• kappa-deformed Spacetime From Twist
• Noncommutative Quantum Hall Effect and Aharonov-Bohm Effect
• The CP(n) Model on Noncommutative Plane
• Gauge Covariance of the Aharonov-Bohm Phase in Noncommutative Quantum Mechanics
• Probing Noncommutativity with Inflationary Gravitational Waves
• The Noncommutative Supersymmetric Nonlinear Sigma Model
• 1+1 Dimensional NCOS and its U(N) Gauge Theory Dual
• Quantum-Gravity Induced Lorentz Violation and Dynamical Mass Generation
• Landau Analog Levels for Dipoles in the Noncommutative Space and Phase Space
• Wess-Zumino-Witten and fermion models in noncommutative space
• Noncommutative Field Theory from twisted Fock space
• On the IR/UV mixing and experimental limits on the parameters of canonical noncommutative spacetimes
• The Compton-Schwarzschild correspondence from extended de Broglie relations
• Noncommutative gauge theories and Lorentz symmetry
• Probing noncommutative theories with quantum optical experiments
• ((F, D1), D3) bound state, S-duality and noncommutative open string/Yang-Mills theory
• The Higgs Mechanism in Non-commutative Gauge Theories
• Energy nonconservation as a link between $f(R,T)$ gravity and noncommutative quantum theory
• Morita Duality and Large-N Limits
• Lorentz Invariance Violation from String Theory
• Noncommutative analogue Aharonov-Bohm effect and superresonance
• Boundaries and the Casimir effect in non-commutative space-time
• CPT Violation and Decoherence in Quantum Gravity
• Spacetime singularity resolution in Snyder noncommutative space
• Some properties of the integrable noncommutative sine-Gordon system
• Spectral Representation and Dispersion Relations in Field Theory on Noncommutative Space
• CMB statistics in noncommutative inflation
• Twisted Covariant Noncommutative Self-dual Gravity
• Natural Cutoffs via Compact Symplectic Manifolds
• On second quantization on noncommutative spaces with twisted symmetries
• Three Body Bound State in Non-Commutative Space
• Real and virtual photons in an external constant electromagnetic field of most general form
• Tensor model and dynamical generation of commutative nonassociative fuzzy spaces
• Schwinger Model In Noncommutating Space-Time
• Perturbative Approach to Higher Derivative Theories with Fermions
• A Membrane Action for OM Theory
• On the UV renormalizability of noncommutative field theories
• Noncommutative Quantum Field Theory: A Confrontation of Symmetries
• On general properties of Lorentz invariant formulation of noncommutative quantum field theory
• Non--Commutative Field Theories beyond Perturbation Theory
• SL(2, Z) Duality and 4-Dimensional Noncommutative Theories
• The BV Formalization of Chern-Simons Theory on Deformed Superspace
• Positronium Hyperfine Splitting in Non-commutative Space at the Order ${\alpha }^6$
• Failure of microcausality in quantum field theory on noncommutative spacetime
• Deformed Super-Yang-Mills in Batalin-Vilkovisky Formalism
• The Z--> l^+ l^- and W--> nu_l l^+ decays in the noncommutative standard model}}
• Comments on Noncommutative Open String Theory: V-duality and Holography
• Noncommutative spaces, the quantum of time and the Lorentz symmetry
• An Interpretation of Noncommutative Field Theory in Terms of a Quantum Shift
• Non-Commutative Open (p,q)-String Theories
• Effective String Tension and Renormalizability: String Theory in a Noncommutative Space
• The Noncommutative S-Matrix
• Space-time non-commutativity tends to create bound states
• The low energy limit of the non-commutative Wess-Zumino model
• Scattering of spin 1/2 particles by the 2+1 dimensional noncommutative Aharonov-Bohm potential
• Noncommutative Chern-Simons Soliton
• Euler Top Dynamics of Nambu-Goto P-Branes
• Renormalizability and Phenomenology of theta-expanded Noncommutative Gauge Field Theory
• IR Dynamics from UV Divergences: UV/IR Mixing, NCFT, and the Hierarchy Problem
• Galilean symmetry in noncommutative Gravitational Quantum Well
• On duality of the noncommutative extension of the Maxwell-Chern-Simons model
• Noncommutative Supersymmetric/Integrable Models and String Theory
• Non-commutative Geometry Modified Non-Gaussianities of Cosmological Perturbation
• Free-fall in a uniform gravitational field in non-commutative quantum mechanics
• Divergences in Non-Commutative Gauge Theories with the Slavnov Term
• Moving mirrors and black hole evaporation in non-commutative space-times
• Bosonized noncommutative bi-fundamental fermion and S-duality
• Noncommutative Tachyon Kinks as D$(p-1)$-branes from Unstable D$p$-brane
• A New Derivation of the CPT and Spin-Statistics Theorems in Non-Commutative Field Theories
• Analyticity and Forward Dispersion Relations in Noncommutative Quantum Field Theory
• On space-time noncommutative theories at finite temperature
• On the mass spectrum of noncommutative Schwinger model in Euclidean ${\mathbb{R}}^2$ space
• Non-Relativistic Non-BPS Dp-brane
• Experimental test of Non-Commutative Quantum Gravity by VIP-2 Lead
• Maximally localized states and causality in non commutative quantum theories
• Holography and D3-branes in Melvin Universes
• The inclusive b -> s γdecay in the noncommutative standard model
• Longitudinal nonlocality in the string S-matrix
• Hamiltonian embedding of the massive noncommutative U(1) theory
• Duality Rotations and BPS Monopoles with Space and Time Noncommutativity
• On the continuity of the commutative limit of the 4d N=4 non-commutative super Yang-Mills theory
• Lorentz symmetry breaking in the noncommutative Wess-Zumino model: One loop corrections
• Varying dilaton as a tracer of classical string interactions
• Discrete Symmetries In Lorentz-Invariant Non-Commutative QED
• Extending general covariance: Moyal-type noncommutative manifolds
• Infrared cutoffs and the adiabatic limit in noncommutative spacetime
• Ultrahyperfunctional Approach to Non-Commutative Quantum Field Theory
• Thermodynamics of a charged particle in a noncommutative plane in a background magnetic field
• Domain wall solitons and Hopf algebraic translational symmetries in noncommutative field theories
• Noncommutative Maxwell-Chern-Simons theory (I): One-loop dispersion relation analysis
• Cutting rules and perturbative unitarity of noncommutative electric-type field theories from string theory
• Charged rotating BTZ black holes in noncommutative spaces and torsion gravity
• On the unitarity of higher-dervative and nonlocal theories
• The noncommutative QED threshold energy versus the optimum collision energy
• CMB statistical anisotropy from noncommutative gravitational waves
• High-Energy gamma-ray Astronomy and String Theory
• A Note on Unitarity of Non-Relativistic Non-Commutative Theories
• Analyticity of the Scattering Amplitude, Causality and High-Energy Bounds in Quantum Field Theory on Noncommutative Space-Time
• Consistent Anomalies in Translation-Invariant Noncommutative Gauge Theories
• Gravitational collapse of spherically symmetric stars in noncommutative general relativity
• Perturbation theory of the space-time non-commutative real scalar field theories
• Canonical analysis of space-time noncommutative theories and gauge symmetries
• Canonical formalism and quantization of perturbative sector of higher-derivative theories
• Tree Unitarity and Partial Wave Expansion in Noncommutative Quantum Field Theory
• High-Temperature Effective Potential of Noncommutative Scalar Field Theory: Reduction of Degree of Freedom by Noncommutativity
• Field Theory on a Non-commutative Plane: a Non-Perturbative Study
• On beta-deformations and Noncommutativity
• Noncommutative of space-time and the relativistic Hydrogen atom
• Failure of microcausality in noncommutative field theories
• Magnetic Monopole in Noncommutative Space-Time and Wu-Yang Singularity-Free Gauge Transformations
• Inferring type and scale of noncommutativity from the PTOLEMY experiment
• Lax pair and Darboux transformation of noncommutative U(N) principal chiral model
• On Duality Rotations in Light-Like Noncommutative Electromagnetism
• On the consequences of twisted Poincare' symmetry upon QFT on Moyal noncommutative spaces
• Heat kernel of non-minimal gauge field kinetic operators on Moyal plane
• Induced magnetic moment in noncommutative Chern-Simons scalar QED
• Light-Like Noncommutativity, Light-Front Quantization and New Light on UV/IR Mixing
• Space/Time Noncommutativity in String Theories without Background Electric Field
• Perturbative quantization of two-dimensional space-time noncommutative QED
• Time reversal and rotational symmetries in noncommutative phase space
• Noncommutative Time in Quantum Field Theory
• Noncommutative (supersymmetric) electrodynamics in the Yang-Feldman formalism
• A Generalization of Slavnov-Extended Non-Commutative Gauge Theories
• The form factors existing in the b->s g^* decay and the possible CP violating effects in the noncommutative standard model
• Noncommutativity of Space and Rotation of Polarization of Light in a Background Magnetic Field
• String Backgrounds of the Yang-Baxter Deformed $Ad{S}_4\times {\mathbb{CP}}^3$ Superstring
• Probes for String-Inspired Foam, Lorentz, and CPT Violations in Astrophysics
• The Hierarchy Problem: From the Fundamentals to the Frontiers
• Non-commutative Space And Chan-Paton Algebra In Open String Field Algebra
• One Loop Renormalizability of Spontaneously Broken Gauge Theory with a Product of Gauge Groups on Noncommutative Spacetime: the U(1) x U(1) Case
• Stringy Space-Time Foam and High-Energy Cosmic Photons
• Källén-Lehmann representation of noncommutative quantum electrodynamics
• Conserved Quantities in Noncommutative Principal Chiral Model with Wess-Zumino Term
• Enveloping algebra Noncommutative SM: Renormalisability and High Energy Physics Phenomenology
• One-loop unitarity of scalar field theories on Poincare invariant commutative nonassociative spacetimes
• The Galilean Nature of V-duality for Noncommutative Open String and Yang-Mills Theories
• Constraints, gauge symmetries, and noncommutative gravity in two dimensions
• A Novel Foamy Origin for Singlet Fermion Masses
• Canonical Quantization, Space-Time Noncommutativity and Deformed Symmetries in Field Theory
• Possible Detection of Causality Violation in a Non-local Scalar Model
• Noncommutative Coordinates Invariant under Rotations and Lorentz Transformations
• Causality in Non-Commutative Quantum Field Theories
• Three-dimensional noncommutative Yukawa theory: Induced effective action and propagating modes
• Non-Anticommutative Quantum Gravity
• Constraints to Lorentz violation and ultrahigh-energy electrons in D-foamy space-times
• Some considerations on duality concerning kappa-Minkowski spacetime theories
• Wave Propagation and IR/UV Mixing in Noncommutative Spacetimes
• Translation-Invariant Noncommutative Gauge Theories, Matrix Modeling and Noncommutative Geometry
• An Associative and Noncommutative Product for the Low Energy Effective Theory of a D-Brane in Curved Backgrounds and Bi-Local Fields
• Space-time noncommutativity and (1+1) Higgs Model
• New aspects of quantization of Jackiw-Pi model: field-antifield formalism and noncommutativity
• Time-Delay at Higher Genus in High-Energy Open String Scattering
• On Finite Noncommutativity in Quantum Field Theory
• Jost-Lehmann-Dyson Representation, Analyticity in Angle Variable and Upper Bounds in Noncommutative Quantum Field Theory
• Towards an Axiomatic Formulation of Noncommutative Quantum Field Theory. II
• Symmetry breaking in nonuniform noncommutative $\lambda {\varphi }^4$ theory at finite temperature
• New M(atrix)-models for Commutative and Noncommutative Gauge Theories
• $\mathcal{O}(\theta )$ Feynman rules for quadrilinear gauge boson couplings in noncommutative standard model
• Horizon Branes and Chiral Strings
• One-loop unitarity of string theories in a constant external background and their Seiberg-Witten limit
• Haag's Theorem in Noncommutative Quantum Field Theory
• Electromagnetic Dualities on Noncommutative Space-Time and Symplectic Formalisms
• Irreducibility of the set of field operators in Noncommutative Quantum Field Theory
• Phase Space Non-commutativity and its Stability
• ${\pi }^{+}{\pi }^{+}$ and ${\pi }^{+}{\pi }^{-}$ colliding in noncommutative space
• Aspects of noncommutativity in field theory, strings and membranes
• A note on the fuzzy sphere area spectrum, black hole luminosity, and the quantum nature of spacetime
• On space-time noncommutative U(1) model at high temperature