Pauli-Jordan Function and Scalar Field Quantization in $\kappa$-Minkowski Noncommutative Spacetime

Abstract

We study a complex free scalar field theory on a noncommutative background spacetime called $\kappa$-Minkowski. In particular we address the problem of second quantization. We obtain the algebra of creation and annihilation operators in an explicitly covariant way. Our procedure does not use canonical/Hamiltonian formulations, which turn out to be ill-defined in our context. Instead we work in a spacetime covariant way by introducing a noncommutative Pauli-Jordan function. This function is obtained as a generalization of the ordinary, commutative, one by taking into account the constraints imposed by the symmetries of our noncommutative spacetime. The Pauli-Jordan function is later employed to study the structure of the light cone in $\kappa$-Minkowski spacetime, and to draw conclusions on the superluminal propagation of signals.

arXiv comment28 pages (+7 of appendices), 10 figures; added appendix on the derivation of finite kappa-Poincaré transformations of momentum space from the quantum group's commutation relations, updated references

References in corpus (59)

• Potential Sensitivity of Gamma-Ray Burster Observations to Wave Dispersion in Vacuo
• Lorentz invariance with an invariant energy scale
• Relativity in space-times with short-distance structure governed by an observer-independent (Planckian) length scale
• Nonstandard optics from quantum spacetime
• Quantum Spacetime Phenomenology
• Generalized Lorentz invariance with an invariant energy scale
• Testing Einstein's special relativity with Fermi's short hard gamma-ray burst GRB090510
• Distance Measurement and Wave Dispersion in a Liouville-String Approach to Quantum Gravity
• 3d Quantum Gravity and Effective Non-Commutative Quantum Field Theory
• Quantum $\kappa$-Poincare in Any Dimensions
• Deformed Boost Transformations That Saturate at the Planck Scale
• Astrophysical Probes of the Constancy of the Velocity of Light
• Prospects for Large Relativity Violations in Matter-Gravity Couplings
• Robust Limits on Lorentz Violation from Gamma-Ray Bursts
• String theories with deformed energy momentum relations, and a possible non-tachyonic bosonic string
• Derivation of a Vacuum Refractive Index in a Stringy Space-Time Foam Model
• Quantum Mechanics of a Point Particle in 2+1 Dimensional Gravity
• Deformed Field Theory on kappa-spacetime
• Doubly Special Relativity and de Sitter space
• Local D=4 Field Theory on $\kappa$--Deformed Minkowski Space
• Twisted Statistics in kappa-Minkowski Spacetime
• Limits on the Measurability of Space-time Distances in (the Semi-classical Approximation of) Quantum Gravity
• A Microscopic Recoil Model for Light-Cone Fluctuations in Quantum Gravity
• Synchrotron Radiation from the Crab Nebula Discriminates between Models of Space-Time Foam
• Poisson structures on the Poincare group
• Conservation Laws in Doubly Special Relativity
• Waves on Noncommutative Spacetime and Gamma-Ray Bursts
• Fock space, quantum fields and kappa-Poincaré symmetries
• Field theory on $\kappa$--Minkowski space revisited: Noether charges and breaking of Lorentz symmetry
• Towards Quantum Noncommutative $\kappa$-deformed Field Theory
• From noncommutative kappa-Minkowski to Minkowski space-time
• Hopf-algebra description of noncommutative-spacetime symmetries
• Rainbow gravity and scale-invariant fluctuations
• Speed of particles and a relativity of locality in $\kappa$-Minkowski quantum spacetime
• Covariant particle statistics and intertwiners of the kappa-deformed Poincare algebra
• Generalized Weyl systems and kappa-Minkowski space
• IceCube and GRB neutrinos propagating in quantum spacetime
• Dirac spinors for Doubly Special Relativity and $\kappa$-Minkowski noncommutative spacetime
• Symplectic geometry and Noether charges for Hopf algebra space-time symmetries
• Interpreting doubly special relativity as a modified theory of measurement
• Lorentz invariant field theory on kappa-Minkowski space
• Comments on Graviton Propagation in Light of GW150914
• A no-pure-boost uncertainty principle from spacetime noncommutativity
• Noncommutative Spaces and Poincaré Symmetry
• Anatomy of a deformed symmetry: field quantization on curved momentum space
• $\kappa$--deformed Wigner construction of relativistic wave functions and free fields on $\kappa$-Minkowski space
• Rainbow statistics
• A twisted look on kappa-Minkowski: U(1) gauge theory
• Discreteness of area in noncommutative space
• U(1) gauge field theory on kappa-Minkowski space
• Kappa-deformed oscillators, the choice of star product and free kappa-deformed quantum fields
• Algebraic approach to quantum gravity II: noncommutative spacetime
• On alternative approaches to Lorentz violation in loop quantum gravity inspired models
• Physical Constraints on Quantum Deformations of Spacetime Symmetries
• Beyond Fock space in three dimensional semiclassical gravity
• AdS Poisson homogeneous spaces and Drinfel'd doubles
• A short introduction to $\kappa$-deformation
• Canonical k-Minkowski Spacetime
• Past and future blurring at fundamental length scale

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• $\kappa$-Poincaré-comodules, Braided Tensor Products and Noncommutative Quantum Field Theory
• Light Cone in a Quantum Spacetime
• Doubly special relativity as a non-local quantum field theory
• Multiparticle states in braided lightlike $\kappa$-Minkowski noncommutative QFT
• Quantum causality constraints on kappa-Minkowski space-time
• The Weyl-Mellin quantization map for $\kappa$-Minkowski Noncommutative Spacetime
• Quantum causality in $\kappa$-Minkowski and related constraints
• On the UV/IR mixing of Lie algebra-type noncommutatitive ${\varphi }^4$-theories
• Noncommutative Lightcones from Quantum SO(2,1) Conformal Groups
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