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

• URL: http://arxiv.org/abs/2312.10971v1
• Date: Mon, 18 Dec 2023 06:54:56 GMT
• Title: Characterizing Klein-Fock-Gordon-Majorana particles in (1+1) dimensions
• Authors: Salvatore De Vincenzo
• Abstract summary: We write first-order equations in the time derivative that do not have a Hamiltonian form. We examine the nonrelativistic limit of one of the first-order 1D Majorana equations.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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