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.

28 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 (22)

• Prospects for Large Relativity Violations in Matter-Gravity Couplings
• Derivation of a Vacuum Refractive Index in a Stringy Space-Time Foam Model
• Twisted Statistics in kappa-Minkowski Spacetime
• 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
• Speed of particles and a relativity of locality in $\kappa$-Minkowski quantum spacetime
• Covariant particle statistics and intertwiners of the kappa-deformed Poincare algebra
• Symplectic geometry and Noether charges for Hopf algebra space-time symmetries
• 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
• Rainbow statistics
• Discreteness of area in noncommutative space
• Kappa-deformed oscillators, the choice of star product and free kappa-deformed quantum fields
• Algebraic approach to quantum gravity II: noncommutative spacetime
• Physical Constraints on Quantum Deformations of Spacetime Symmetries
• AdS Poisson homogeneous spaces and Drinfel'd doubles
• Canonical k-Minkowski Spacetime
• A short introduction to $\kappa$-deformation
• Past and future blurring at fundamental length scale

Cited by in corpus (17)

• Localization and Reference Frames in $\kappa$-Minkowski Spacetime
• Gauge theories on $\kappa$-Minkowski spaces: Twist and modular operators
• $\kappa$-deformed complex fields and discrete symmetries
• The Momentum Spaces of $\kappa$-Minkowski noncommutative spacetime
• Geometrizing the Klein-Gordon and Dirac equations in Doubly Special Relativity
• Signal propagation on $\kappa$-Minkowski spacetime and non-local two-point functions
• Interplay between spacetime curvature, speed of light and quantum deformations of relativistic symmetries
• $\kappa$-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
• Algebraic structures in $\kappa$-Poincaré invariant gauge theories