Cubic root of Klein-Gordon equation

Abstract

We construct new relativistic linear differential equation in $d$ dimensions generalizing Dirac equation by employing the Clifford algebra of the cubic polynomial associated to Klein-Gordon operator multiplied by the mass parameter. Unlike the Dirac case where the spin content is unique and Lorentz covariance is manifest, here the spin as well as Lorentz covariance of the theory are related to the choice of representation of the Clifford algebra. One of the considered explicit matrix representations gives rise to anyon-like fields in $d=1+1$. Coupling to a U(1) gauge field is discussed and compared with Dirac theory.

12 pages, typos corrected. To appear in Phys. Lett. B

Cited by in corpus (14)

• Review of Some Promising Fractional Physical Models
• Relativistic wave equations with fractional derivatives and pseudo-differential operators
• Fractional helicity, Lorentz symmetry breaking, compactification and anyons
• Field Theoretic Realizations for Cubic Supersymmetry
• Extending the D'Alembert Solution to Space-Time Modified Riemann-Liouville Fractional Wave Equations
• Repulsive Casimir Force from Fractional Neumann Boundary Conditions
• Z${}_3$-graded differential geometry of quantum plane
• Finite Temperature Casimir Effect for a Massless Fractional Klein-Gordon field with Fractional Neumann Conditions
• Topological symmetry breaking of self--interacting fractional Klein--Gordon field on toroidal spacetime
• The partially alternating ternary sum in an associative dialgebra
• Third order wave equation in Duffin-Kemmer-Petiau theory. Massive case
• Ternary Z2 x Z3 graded algebras and ternary Dirac equation
• Anomalous g-Factors for Charged Leptons in a Fractional Coarse-Grained Approach
• Extension of the Poincaré Symmetry and Its Field Theoretical Implementation