Spin-Statistics and CPT Theorems in Noncommutative Field Theory

Abstract

We show that Pauli's spin-statistics relation remains valid in noncommutative quantum field theories (NC QFT), with the exception of some peculiar cases of noncommutativity between space and time. We also prove that, while the individual symmetries C and T, and in some cases also P, are broken, the CPT theorem still holds in general for noncommutative field theories, in spite of the inherent nonlocality and violation of Lorentz invariance.

5 pages, latex, no figures

References in corpus (1)

• The quantum structure of spacetime at the Planck scale and quantum fields

Cited by in corpus (79)

• Quantum Spacetime Phenomenology
• On a Lorentz-Invariant Interpretation of Noncommutative Space-Time and Its Implications on Noncommutative QFT
• Ponzano-Regge model revisited III: Feynman diagrams and Effective field theory
• New concept of relativistic invariance in NC space-time: twisted Poincaré symmetry and its implications
• General Properties of Noncommutative Field Theories
• Twisted Statistics in kappa-Minkowski Spacetime
• Deformed Oscillator Algebras and QFT in $\kappa$-Minkowski Spacetime
• CPT Violation Does Not Lead to Violation of Lorentz Invariance and Vice Versa
• A Realization of the Cohen-Glashow Very Special Relativity
• Twist and Spin-Statistics Relation in Noncommutative Quantum Field Theory
• Noncommutative Quantum Field Theories
• Towards an Axiomatic Formulation of Noncommutative Quantum Field Theory
• kappa-deformed Spacetime From Twist
• Cosmic Rays and the Search for a Lorentz Invariance Violation
• Path Integral for Space-time Noncommutative Field Theory
• Gauge Covariance of the Aharonov-Bohm Phase in Noncommutative Quantum Mechanics
• Quantum field theory based on birefringent modified Maxwell theory
• Kappa-Minkowski spacetime, Kappa-Poincaré Hopf algebra and realizations
• Noncommutative Field Theory from twisted Fock space
• $t\to bW$ in NonCommutative Standard Model
• Noncommutative Synchrotron
• Noncommutativity and theta-locality
• Finite temperature phase transition of a single scalar field on a fuzzy sphere
• Noncommutative Quantum Field Theory: A Confrontation of Symmetries
• On general properties of Lorentz invariant formulation of noncommutative quantum field theory
• Testing Noncommutative Spacetimes and Violations of the Pauli Exclusion Principle with underground experiments
• Quantum statistics and noncommutative black holes
• Failure of microcausality in quantum field theory on noncommutative spacetime
• An Interpretation of Noncommutative Field Theory in Terms of a Quantum Shift
• Quasinormal Modes in Noncommutative Schwarzschild black holes
• Noncommutative QED corrections to e^+e^-\toγγγat linear collider energies
• Lorentz-invariant CPT violation
• IR Dynamics from UV Divergences: UV/IR Mixing, NCFT, and the Hierarchy Problem
• A New Derivation of the CPT and Spin-Statistics Theorems in Non-Commutative Field Theories
• Free-fall in a uniform gravitational field in non-commutative quantum mechanics
• Analyticity and Forward Dispersion Relations in Noncommutative Quantum Field Theory
• Experimental test of Non-Commutative Quantum Gravity by VIP-2 Lead
• Uniformly accelerated detector in the $\kappa$-deformed Dirac vacuum
• The coupling of fermions to the three-dimensional noncommutative $C{P}^{N-1}$ model: minimal and supersymmetric extensions
• Discrete symmetries in the Kaluza-Klein-like theories
• Running of the Spectral Index in Noncommutative Inflation
• Lorentz symmetry breaking in the noncommutative Wess-Zumino model: One loop corrections
• Infrared cutoffs and the adiabatic limit in noncommutative spacetime
• Constrains of Charge-to-Mass Ratios on Noncommutative Phase Space
• Analyticity of the Scattering Amplitude, Causality and High-Energy Bounds in Quantum Field Theory on Noncommutative Space-Time
• Planck Scale Physics, Gravi-Weak Unification and the Higgs Inflation
• Magnetic Monopole in Noncommutative Space-Time and Wu-Yang Singularity-Free Gauge Transformations
• (2+1)D Noncommutative CP${}^{N-1}$ Model
• Spin-Statistics Violations in Superstring Theory
• Failure of microcausality in noncommutative field theories
• Heat kernel of non-minimal gauge field kinetic operators on Moyal plane
• Scattering in Noncommutative Quantum Mechanics
• Noncommutative Decrumpling Inflation and Running of the Spectral Index
• Light-Like Noncommutativity, Light-Front Quantization and New Light on UV/IR Mixing
• Twisted Fermionic Oscillator Algebra in $\kappa$-Minkowski space-time
• Noncommutativity of Space and Rotation of Polarization of Light in a Background Magnetic Field
• Symplectic Dirac Equation
• Time reversal and rotational symmetries in noncommutative phase space
• Noncommutative Time in Quantum Field Theory
• Spin-statistics-quantum number connection and supersymmetry
• Symmetries, Microcausality and Physics on Canonical Noncommutative Spacetime
• Dealing with T and CPT violations in mixing as well as direct and indirect CP violations for neutral mesons decaying to two vectors
• Composite Structure and Causality
• The dyon charge in noncommutative gauge theories
• An Arena for Model Building in the Cohen-Glashow Very Special Relativity
• Microcausality of spin-induced noncommutative theories
• Causality in Non-Commutative Quantum Field Theories
• On the detectability of paraparticles beyond bosons and fermions
• Minimal momentum estimation in noncommutative phase space of canonical type with preserved rotational and time reversal symmetries
• Nonequilibrium Dynamics in Noncommutative Spacetime
• Reciprocal of the CPT theorem
• Jost-Lehmann-Dyson Representation, Analyticity in Angle Variable and Upper Bounds in Noncommutative Quantum Field Theory
• $\mathcal{O}(\theta )$ Feynman rules for quadrilinear gauge boson couplings in noncommutative standard model
• On Finite Noncommutativity in Quantum Field Theory
• Towards an Axiomatic Formulation of Noncommutative Quantum Field Theory. II
• The Slavnov-Taylor Identities for the 2+1 Dimensional Noncommutative CP${}^{N-1}$ Model
• Heisenberg quantization for the systems of identical particles and the Pauli exclusion principle in noncommutative spaces
• Non-Commutative GUTs, Standard Model and C,P,T properties from Seiberg-Witten map
• Energy renormalization and integrability within the massive neutrinos model