Interacting gauge fields and the zero-energy eigenstates in two dimensions

TL;DR

This paper explores how zero-energy eigenstates of 2D Schrödinger equations with specific potentials can be interpreted as interacting gauge fields, revealing connections to tachyons, U(1), and SU(3) gauge fields, and analyzing associated massive particles.

Contribution

It introduces a novel interpretation of zero-energy eigenstates as interacting gauge fields in two dimensions, linking them to known gauge theories and particle structures.

Findings

Zero-energy states act as gauge fields with effects expressed as complex factors.

Gauge fields for specific potentials correspond to tachyons, U(1), and SU(3) types.

Massive particles with internal structures are derived from zero-energy states.

Abstract

Gauge fields are formulated in terms of the zero-energy eigenstates of 2-dimensional Schr$\ddot {\rm o}$dinger equations with central potentials $V_a(\rho)=-a^2g_a\rho^{2(a-1)}$ ($a\not=0$, $g_a>0$ and $\rho=\sqrt{x^2+y^2}$). It is shown that the zero-energy states can naturally be interpreted as a kind of interacting gauge fields of which effects are solved as the factors $e^{ig_c\chi_A}$, where $\chi_A$ are complex gauge functions written by the zero-energy eigenfunctions. We see that the gauge fields for $a=1$ are nothing but tachyons that have negative squared-mass $m^2=-g_1$. We also find out U(1)-type gauge fields for $a=1/2$ and SU(3)-type gauge fields for $a=3/2$. Massive particles with internal structures described by the zero-energy states are also studied.