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

Tsunehiro Kobayashi

paper

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

arXiv:hep-th/0503051

Abstract

Gauge fields are formulated in terms of the zero-energy eigenstates of 2-dimensional Schr $o ¨$ dinger equations with central potentials $V_{a} (ρ) = - a^{2} g_{a} ρ^{2 (a - 1)}$ ( $a \neq = 0$ , $g_{a} > 0$ and $ρ = x^{2} + y^{2}$ ). 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 $e^{i g_{c} χ_{A}}$ , where $χ_{A}$ 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.

6pages,6figures