Quantisation of $\kappa$-deformed Dirac equation

Abstract

In this paper, we study the quantisation of Dirac field theory in the $\kappa$-deformed space-time. We adopt a quantisation method that uses only equations of motion for quantising the field. Starting from $\kappa$-deformed Dirac equation, valid up to first order in the deformation parameter $a$, we derive deformed unequal time anti-commutation relation between deformed field and its adjoint, leading to undeformed oscillator algebra. Exploiting the freedom of imposing a deformed unequal time anti-commutation relations between $\kappa$-deformed spinor and its adjoint, we also derive a deformed oscillator algebra. We show that deformed number operator is the conserved charge corresponding to global phase transformation symmetry. We construct the $\kappa$-deformed conserved currents, valid up to first order in $a$, corresponding to parity and time-reversal symmetries of $\kappa$-deformed Dirac equation also. We show that these conserved currents and charges have a mass-dependent correction, valid up to first order in $a$. This novel feature is expected to have experimental significance in particle physics. We also show that it is not possible to construct a conserved current associated with charge conjugation, showing that the Dirac particle and its anti-particle satisfy different equations in $\kappa$-space-time.

arXiv comment18 page, More discussions, calculations and references added

References in corpus (31)

• Noncommutative Perturbative Dynamics
• Testable scenario for Relativity with minimum-length
• Bicrossproduct structure of $\kappa$-Poincare group and non-commutative geometry
• On a Lorentz-Invariant Interpretation of Noncommutative Space-Time and Its Implications on Noncommutative QFT
• A Gravity Theory on Noncommutative Spaces
• Classical and Quantum Mechanics of Free \k Relativistic Systems
• Noncommutative Geometry and Gravity
• Introduction to Doubly Special Relativity
• Quantum $\kappa$-Poincare in Any Dimensions
• Kappa-Minkowski space-time and the star product realizations
• New realizations of Lie algebra kappa-deformed Euclidean space
• Twisted Statistics in kappa-Minkowski Spacetime
• Covariant realizations of kappa-deformed space
• Deformed Oscillator Algebras and QFT in $\kappa$-Minkowski Spacetime
• Gauge theories on the kappa-Minkowski spacetime
• The Quantum Deformed Dirac Equation from the k-Poincare` Algebra
• Electrodynamics on $\kappa$-Minkowski space-time
• Constraints on the quantum gravity scale from kappa - Minkowski spacetime
• Dirac spinors for Doubly Special Relativity and $\kappa$-Minkowski noncommutative spacetime
• Generalized Poincare algebras, Hopf algebras and kappa-Minkowski spacetime
• Generalized kappa-deformed spaces, star-products, and their realizations
• Geodesic equation in $k$-Minkowski spacetime
• Noncommutative Differential Forms on the kappa-deformed Space
• $\kappa$--deformed Wigner construction of relativistic wave functions and free fields on $\kappa$-Minkowski space
• Newton's Equation on the kappa space-time and the Kepler problem
• $\kappa$-deformed Dirac Equation
• Maxwell's equations on the $\kappa$-Minkowski spacetime and Electric-Magnetic duality
• Berry Phase Effects in the dynamics of Dirac Electrons in Doubly Special Relativity Framework
• Particle and Antiparticle sectors in DSR1 and kappa-Minkowski space-time
• Quantisation of Klein-Gordon field in $\kappa$ space-time: deformed oscillators and Unruh effect
• Dirac operator on $\kappa$-Minkowski space bicovariant differential calculus and deformed U(1) gauge theory

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