Towards Quantum Noncommutative $\kappa$-deformed Field Theory

Abstract

We introduce new $\kappa$-star product describing the multiplication of quantized $\kappa$-deformed free fields. The $\kappa$-deformation of local free quantum fields originates from two sources: noncommutativity of space-time and the $\kappa$-deformation of field oscillators algebra - we relate these two deformations. We demonstrate that for suitable choice of $\kappa$-deformed field oscillators algebra the $\kappa$-deformed version of microcausality condition is satisfied, and it leads to the deformation of the Pauli-Jordan commutation function defined by the $\kappa$-deformed mass shell. We show by constructing the $\kappa$-deformed Fock space that the use of $\kappa$-deformed oscillator algebra permits to preserve the bosonic statistics of n-particle states. The proposed star product is extended to the product of $n$ fields, which for $n=4$ defines the interaction vertex in perturbative description of noncommutative quantum $\lambda {\varphi }^4$ field theory. It appears that the classical fourmomentum conservation law is satisfied at the interaction vertices.

LaTeX, 16 pages. V2: some clarifications supplemented, two formulas added. V3: three references added, version in press in Physical Review D

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Cited by in corpus (76)

• Twisted Statistics in kappa-Minkowski Spacetime
• Deformed Oscillator Algebras and QFT in $\kappa$-Minkowski Spacetime
• Scalar Field Theory on Non-commutative Snyder Space-Time
• Classical basis for kappa-Poincare algebra and doubly special relativity theories
• Covariant particle statistics and intertwiners of the kappa-deformed Poincare algebra
• Constraints on the quantum gravity scale from kappa - Minkowski spacetime
• Scalar field theory on kappa-Minkowski spacetime and translation and Lorentz invariance
• Generalized Poincare algebras, Hopf algebras and kappa-Minkowski spacetime
• Composite system in rotationally invariant noncommutative phase space
• Kappa Snyder deformations of Minkowski spacetime, realizations and Hopf algebra
• Kappa-deformed Snyder spacetime
• $\kappa$-Deformed Statistics and Classical Fourmomentum Addition Law
• Pauli-Jordan Function and Scalar Field Quantization in $\kappa$-Minkowski Noncommutative Spacetime
• Rainbow statistics
• Newton's Equation on the kappa space-time and the Kepler problem
• Kappa-Minkowski spacetime, Kappa-Poincaré Hopf algebra and realizations
• $\kappa$-deformed Dirac Equation
• The singularity problem and phase-space noncanonical noncommutativity
• On kappa-deformation and triangular quasibialgebra structure
• Covariant particle exchange for kappa-deformed theories in 1+1 dimensions
• Twists, realizations and Hopf algebroid structure of kappa-deformed phase space
• K-Poincare-Hopf algebra and Hopf algebroid structure of phase space from twist
• Differential algebras on kappa-Minkowski space and action of the Lorentz algebra
• Relativistic Thermodynamics with an Invariant Energy Scale
• Differential Structure on kappa-Minkowski Spacetime Realized as Module of Twisted Weyl Algebra
• $\kappa$-Deformed Phase Space, Hopf Algebroid and Twisting
• Kappa-deformed oscillators, the choice of star product and free kappa-deformed quantum fields
• $\kappa$-deformed complex fields and discrete symmetries
• Quantum statistics and noncommutative black holes
• Testing Noncommutative Spacetimes and Violations of the Pauli Exclusion Principle with underground experiments
• Special Relativity induced by Granular Space
• Entanglement dynamics in $\kappa$-deformed spacetime
• Effect of noncommutativity on the spectrum of free particle and harmonic oscillator in rotationally invariant noncommutative phase space
• $\kappa$-Deformations and Extended $\kappa$-Minkowski Spacetimes
• Star product and interacting fields on $\kappa$-Minkowski space
• Different realizations of kappa-momentum space and relative-locality effect
• Field Theory on Curved Noncommutative Spacetimes
• Universal $\kappa$-Poincaré covariant differential calculus over $\kappa$-Minkowski space
• Differential forms and k-Minkowski spacetime from extended twist
• Quantum deformations of Schwarzschild and Schwarzschild-de Sitter spacetimes
• Rotationally invariant noncommutative phase space of canonical type with recovered weak equivalence principle
• Noncommutative phase space with rotational symmetry and hydrogen atom
• Generalized Heisenberg algebra applied to realizations of the orthogonal, Lorentz and Poincare algebras and their dual extensions
• Noncommutative oscillators from a Hopf algebra twist deformation. A first principles derivation
• Algebraic approach to quantum field theory on a class of noncommutative curved spacetimes
• Quantum particles in non-commutative space-time: an identity crisis
• Translational-invariant noncommutative gauge theory
• Deformed Quantum Phase Spaces, Realizations, Star Products and Twists
• The Weyl realizations of Lie algebras and left-right duality
• Photonic realization of the kappa-deformed Dirac equation
• Symmetric ordering and Weyl realizations for quantum Minkowski spaces
• System of interacting harmonic oscillators in rotationally invariant noncommutative phase space
• Time reversal and rotational symmetries in noncommutative phase space
• Effects of a Maximal Energy Scale in Thermodynamics for Photon Gas and Construction of Path Integral
• Oscillator model on Lie-algebraically deformed nonrelativistic space-time
• Exponential Formulas, Normal Ordering and the Weyl-Heisenberg Algebra
• Generalized Heisenberg algebra, realizations of the $\mathfrak{gl}(n)$ algebra and applications
• Minimal momentum estimation in noncommutative phase space of canonical type with preserved rotational and time reversal symmetries
• Quantization of kappa-deformed free fields and kappa-deformed oscillators
• Neutron Star in Quantized-space-time
• Braided Field Quantization from Quantum Poincare Covariance
• Fate of $\kappa$-Minkowski space-time in non-relativistic (Galilean) and ultra-relativistic (Carrollian) regimes
• Bicrossproduct construction versus Weyl-Heisenberg algebra
• From Noncommutative Sphere to Nonrelativistic Spin
• Noncommutative kappa-Minkowski phi4 theory: Construction, properties and propagation
• Generalization of Weyl realization to a class of Lie superalgebras
• Influence of the cosmological constant on $\kappa$-deformed Neutron Star
• Braided Tensor Products and the Covariance of Quantum Noncommutative Free Fields
• From quantum deformations of relativistic symmetries to modified kinematics and dynamics
• Non-commutative correction of ideal gas thermodynamics
• Harmonic oscillator chain in noncommutative phase space with rotational symmetry
• The energy-momentum conservation law in two-particle system for twist-deformed Galilei Hopf algebras
• Braided algebras and the kappa-deformed oscillators
• Asymmetry in momentum space: restoring $\mathcal{C}\mathcal{P}\mathcal{T}$ invariance of $\kappa$-field theory
• Braided Statistics from Abelian Twist in $\kappa$-Minkowski Spacetime
• The covariant and on-shell statistics in kappa-deformed spacetime