Space-Time Noncommutativity, Discreteness of Time and Unitarity

Abstract

Violation of unitarity for noncommutative field theory on compact space-times is considered. Although such theories are free of ultraviolet divergences, they still violate unitarity while in a usual field theory such a violation occurs when the theory is nonrenormalizable. The compactness of space-like coordinates implies discreteness of the time variable which leads to appearance of unphysical modes and violation of unitarity even in the absence of a star-product in the interaction terms. Thus, this conclusion holds also for other quantum field theories with discrete time. Violation of causality, among others, occurs also as the nonvanishing of the commutation relations between observables at space-like distances with a typical scale of noncommutativity. While this feature allows for a possible violation of the spin-statistics theorem, such a violation does not rescue the situation but makes the scale of causality violation as the inverse of the mass appearing in the considered model, i.e., even more severe. We also stress the role of smearing over the noncommutative coordinates entering the field operator symbols.

10 pages, plain LaTeX

References in corpus (3)

• Noncommutative Perturbative Dynamics
• Space-Time Noncommutative Field Theories And Unitarity
• Hamiltonian Formalism for Space-time Non-commutative Theories

Cited by in corpus (67)

• Hydrogen Atom Spectrum and the Lamb Shift in Noncommutative QED
• UV divergence-free QFT on noncommutative plane
• Review of the Phenomenology of Noncommutative Geometry
• Aharonov-Bohm Effect in Noncommutative Spaces
• Noncommutative Standard Model: Model Building
• Quantum Theories on Noncommutative Spaces with Nontrivial Topology: Aharonov-Bohm and Casimir Effects
• Noncommutative ${\Phi }^4$ Theory at Two Loops
• Twisted Statistics in kappa-Minkowski Spacetime
• Noncommutative QED and Anomalous Dipole Moments
• Perturbative Approach to Higher Derivative and Nonlocal Theories
• Unitary Quantum Physics with Time-Space Noncommutativity
• Cosmological and Black Hole Spacetimes in Twisted Noncommutative Gravity
• Non-Commutativity and Unitarity Violation in Gauge Boson Scattering
• Noncommutative BTZ Black Hole and Discrete Time
• CP violation from noncommutative geometry
• Pair Production by a Constant External Field in Noncommutative QED
• Matrix Model Approach to Cosmology
• Breaking CPT by mixed non-commutativity
• Semi-Leptonic Decay of a Polarized Top Quark in the Noncommutative Standard Model
• Schwarzschild Black Hole in Noncommutative Spaces
• The Hidden Quantum Groups Symmetry of Super-renormalizable Gravity
• Time-Space Noncommutativity: Quantised Evolutions
• Energy nonconservation as a link between $f(R,T)$ gravity and noncommutative quantum theory
• Inertial spin Hall effect in noncommutative space
• CMB statistics in noncommutative inflation
• Junctions of Supersymmetric Tubes
• Signature change in matrix model solutions
• Perturbative Approach to Higher Derivative Theories with Fermions
• Quantum statistics and noncommutative black holes
• The Z--> l^+ l^- and W--> nu_l l^+ decays in the noncommutative standard model}}
• Time Discretization From Noncommutativity
• Matrix Model Cosmology in Two Space-time Dimensions
• Noncommutativity and logarithmic correction to the black hole entropy
• Noncommutativity and Reparametrisation symmetry
• Worldline approach to noncommutative field theory
• Non-commutative Geometry Modified Non-Gaussianities of Cosmological Perturbation
• Constraints on Non-Commutative Physics Scale with Neutrino-Electron Scattering
• On the mass spectrum of noncommutative Schwinger model in Euclidean ${\mathbb{R}}^2$ space
• On space-time noncommutative theories at finite temperature
• The inclusive b -> s γdecay in the noncommutative standard model
• Double Quantization
• Single top quark production in $t$-channel at the LHC in Noncommutative Space-Time
• Metric perturbations in Noncommutative Gravity
• Noncommutative Standard Model in Top Quark Sector
• Noncommutative correction to the entropy of charged BTZ black hole
• Discrete Time Evolution and Energy Nonconservation in Noncommutative Physics
• On the Meaning of the String-Inspired Noncommutativity and its Implications
• Fingerprints of the quantum space-time in time-dependent quantum mechanics: An emergent geometric phase
• Consistent Anomalies in Translation-Invariant Noncommutative Gauge Theories
• Noncommutative Static Strings from Matrix Models
• Tree Unitarity and Partial Wave Expansion in Noncommutative Quantum Field Theory
• Relativistic Particles on Quantum Space-time
• Gravitational probe of quantum spacetime
• The form factors existing in the b->s g^* decay and the possible CP violating effects in the noncommutative standard model
• On the Failure of Spin-Statistics Connection in Quantum Gravity
• Quantum dot with spin-orbit interaction in noncommutative phase space and analog Landau levels
• Noncommutative Coordinates Invariant under Rotations and Lorentz Transformations
• Some considerations on duality concerning kappa-Minkowski spacetime theories
• Symmetry Reduction and Exact Solutions in Twisted Noncommutative Gravity
• The Angular Correlations in Top Quark Decays in Standard Model Extensions
• Search for noncommutative interactions in $\gamma \gamma \to \gamma \gamma$ process at the LHC
• Gauge theory solitons on noncommutative cylinder
• Domain walls between gauge theories
• Waves on Noncommutative Spacetimes
• Entropy of black holes, charged probes and noncommutative generalization
• Quantum mechanics and field theory with momentum defined on an anti-de-Sitter space
• Some Aspects of Scattering in (Non) Commutative Gauge Theories