Characterizing Klein-Fock-Gordon-Majorana particles in (1+1) dimensions

Abstract

Theoretically, in (1+1) dimensions, one can have Klein-Fock-Gordon-Majorana (KFGM) particles. More precisely, these are one-dimensional (1D) Klein-Fock-Gordon (KFG) and Majorana particles at the same time. In principle, the wave equations considered to describe such first-quantized particles are the standard 1D KFG equation and/or the 1D Feshbach-Villars (FV) equation, each with a real Lorentz scalar potential and some kind of Majorana condition. The aim of this paper is to analyze the latter assumption fully and systematically; additionally, we introduce specific equations and boundary conditions to characterize these particles when they lie within an interval (or on a line with a tiny hole at a point). In fact, we write first-order equations in the time derivative that do not have a Hamiltonian form. We may refer to these equations as first-order 1D Majorana equations for 1D KFGM particles. Moreover, each of them leads to a second-order equation in time that becomes the standard 1D KFG equation when the scalar potential is independent of time. Additionally, we examine the nonrelativistic limit of one of the first-order 1D Majorana equations.

26 pages

References in corpus (5)

• Introduction to topological superconductivity and Majorana fermions
• Effective theories for a nonrelativistic field in an expanding universe: Induced self-interaction, pressure, sound speed, and viscosity
• Real scalar field, non-relativistic limit, and cosmological expansion
• General pseudo self-adjoint boundary conditions for a 1D KFG particle in a box
• On wave equations for the Majorana particle in (3+1) and (1+1) dimensions