The Quantum Deformed Dirac Equation from the k-Poincare` Algebra

Abstract

In this letter we derive a deformed Dirac equation invariant under the k-Poincare` quantum algebra. A peculiar feature is that the square of the k-Dirac operator is related to the second Casimir (the k-deformed squared Pauli-Lubanski vector). The ``spinorial'' realization of the k-Poincare` is obtained by a contraction of the coproduct of the real form of SO_q(3,2) using the 4-dimensional representation which results to be, up some scalar factors, the same of the undeformed algebra in terms of the usual gamma matrices.

6 pages, Latex

Cited by in corpus (37)

• Bicrossproduct structure of $\kappa$-Poincare group and non-commutative geometry
• Deformed Field Theory on kappa-spacetime
• Noncommutative Differential Calculus on the Kappa-Minkowski Space
• Gravity-wave interferometers as probes of a low-energy effective quantum gravity
• Classical basis for kappa-Poincare algebra and doubly special relativity theories
• Generalized Weyl systems and kappa-Minkowski space
• Dirac spinors for Doubly Special Relativity and $\kappa$-Minkowski noncommutative spacetime
• Effects of quantum deformation on the spin-1/2 Aharonov-Bohm problem
• On the $\kappa$-Dirac Oscillator revisited
• Derivatives, forms and vector fields on the kappa-deformed Euclidean space
• $\kappa$--deformed Wigner construction of relativistic wave functions and free fields on $\kappa$-Minkowski space
• The Dirac-Coulomb Problem for the $\kappa$-Poincare Quantum Group
• $\kappa$-deformed Dirac Equation
• Quantum Deformation of the Poincare Supergroup and $\kappa$-deformed Superspace
• Differential calculi on quantum Minkowski space
• Representation Theory of Quantized Poincare Algebra. Tensor Operators and Their Application to One-Partical Systems
• A modular spectral triple for $\kappa$-Minkowski space
• Spectral geometry of $\kappa$-Minkowski space
• The 2D $\kappa$-Dirac oscillator
• Geometrizing the Klein-Gordon and Dirac equations in Doubly Special Relativity
• Interplay between spacetime curvature, speed of light and quantum deformations of relativistic symmetries
• Particle and Antiparticle sectors in DSR1 and kappa-Minkowski space-time
• Effects of quantum deformation on the integer quantum Hall effect
• Influence of the dispersion relation on the Unruh effect according to the relativistic Doppler shift method
• Effects of quantum deformation on the Jaynes-Cummings and anti-Jaynes-Cummings models
• Dirac operator on $\kappa$-Minkowski space bicovariant differential calculus and deformed U(1) gauge theory
• Kappa-deformed Dirac oscillator in an external magnetic field
• Photonic realization of the kappa-deformed Dirac equation
• Twisted Fermionic Oscillator Algebra in $\kappa$-Minkowski space-time
• Doubly special relativity as a non-local quantum field theory
• Propagation of spinors on a noncommutative spacetime: equivalence of the formal and the effective approach
• Nonlocal field theory driven by a deformed product. Generalization of Kalb-Ramond duality
• Non-local quantum field theory from doubly special relativity
• Quantisation of $\kappa$-deformed Dirac equation
• Formal developments in curved momentum space: the quantum field theory roadmap
• Path integral quantization of a spinning particle
• Quantum Deformations of Space-Time Symmetries with Mass-Like Deformation Parameter