On the groundstate of octonionic matrix models in a ball

TL;DR

This paper investigates the existence and uniqueness of the groundstate wavefunction in an octonionic matrix model with SU(N) and G2 symmetry on a bounded domain, using mathematical theorems and explicit arguments.

Contribution

It provides a rigorous proof of existence and uniqueness of the groundstate for a specific octonionic matrix model, which was previously unestablished.

Findings

Existence of the groundstate wavefunction is proven.

Uniqueness of the groundstate is demonstrated through explicit arguments.

The Lax-Milgram theorem is applied to establish existence.

Abstract

In this work we examine the existence and uniqueness of the groundstate of a SU(N)x G2 octonionic matrix model on a bounded domain of R^N. The existence and uniqueness argument of the groundstate wavefunction follows from the Lax-Milgram theorem. Uniqueness is shown by means of an explicit argument which is drafted in some detail.