Cubic root of Klein-Gordon equation

  title={Cubic root of Klein-Gordon equation},
  author={Mikhail S. Plyushchay and Michel Rausch de Traubenberg},
  journal={Physics Letters B},

Relativistic wave equations with fractional derivatives and pseudodifferential operators

We study the class of the free relativistic covariant equations generated by the fractional powers of the d′Alembertian operator (□1/n). The equations corresponding to n=1 and 2 (Klein-Gordon and

Field Theoretic Realizations for Cubic Supersymmetry

We consider a four-dimensional space–time symmetry which is a nontrivial extension of the Poincare algebra, different from supersymmetry and not contradicting a priori the well-known no-go theorems.

Topological symmetry breaking of self-interacting fractional Klein–Gordon field theories on toroidal spacetime

Quartic self-interacting fractional Klein–Gordon scalar massive and massless field theories on toroidal spacetime are studied. The effective potential and topologically generated mass are determined


Fractional calculus has recently attracted considerable attention. In particular, various fractional differential equations are used to model nonlinear wave theory that arises in many different areas

Extension of the Poincaré Symmetry and Its Field Theoretical Implementation

We define a new algebraic extension of the Poincar\'e symmetry; this algebra is used to implement a field theoretical model. Free Lagrangians are explicitly constructed; several discussions regarding

Ternary Z2 × Z3 Graded Algebras and Ternary Dirac Equation

  • R. Kerner
  • Mathematics
    Physics of Atomic Nuclei
  • 2018
The wave equation generalizing the Dirac operator to the Z3-graded case is introduced, whose diagonalization leads to a sixth-order equation. It intertwines not only quark and anti-quark state as

Casimir Effect Associated with Fractional Klein-Gordon Field

This paper gives a brief review on the recent work on fractional Klein-Gordon fields, in particular on the Casimir effect associated to fractional Klein-Gordon fields in various geometries and



R-Deformed Heisenberg Algebra, Anyons and D=2+1 Supersymmetry

A universal minimal spinor set of linear differential equations describing anyons and ordinary integer and half-integer spin fields is constructed with the help of deformed Heisenberg algebra with

Linear differential equations for a fractional spin field

The vector system of linear differential equations for a field with arbitrary fractional spin is proposed using infinite‐dimensional half‐bounded unitary representations of the SL(2,R) group. In the

Local Fractional Supersymmetry for Alternative Statistics

A group theory justification of one-dimensional fractional supersymmetry is proposed using an analog of a coset space, just like the one introduced in 1-D supersymmetry. This theory is then gauged to

The Particle Aspect of Meson Theory

1. Introduction For many years a central problem of theoretical physics has been to set up a satisfactory relativistic theory of elementary particles. This problem is yet far from solution, the

Anyons as spinning particles

A model-independent formulation of anyons as spinning particles is presented. The general properties of the classical theory of (2+1)-dimensional relativistic fractional spin particles and some