Physical Vacuum Properties and Internal Space Dimension

TL;DR

This paper explores the properties of matrix spaces defined by Dirac matrices in various dimensions, focusing on vacuum states and their realizations, and concludes that 11-dimensional space is fundamental for physics based on vacuum energy considerations.

Contribution

It introduces new vacuum system realizations in matrix spaces, especially highlighting the significance of 7- and 11-dimensional spaces in physical theories.

Findings

Two vacuum realizations in 7D space: orthonormal and E8 root basis.

The minimal dimension for physically relevant space is identified as 11D.

Vacuum energy density considerations support 11D space as fundamental.

Abstract

The paper addresses matrix spaces, whose properties and dynamics are determined by Dirac matrices in Riemannian spaces of different dimension and signature. Among all Dirac matrix systems there are such ones, which nontrivial scalar, vector or other tensors cannot be made up from. These Dirac matrix systems are associated with the vacuum state of the matrix space. The simplest vacuum system realization can be ensured using the orthonormal basis in the internal matrix space. This vacuum system realization is not however unique. The case of 7-dimensional Riemannian space of signature 7(-) is considered in detail. In this case two basically different vacuum system realizations are possible: (1) with using the orthonormal basis; (2) with using the oblique-angled basis, whose base vectors coincide with the simple roots of algebra E_{8}. Considerations are presented, from which it follows that the least-dimension space bearing on physics is the Riemannian 11-dimensional space of signature 1(-)& 10(+). The considerations consist in the condition of maximum vacuum energy density and vacuum fluctuation energy density.