Fundamental Fields as Eigenvectors of the Metric Tensor in a 16-Dimensional Space-Time

• 作者: Alberto Strumia
• 来源期刊: 应用数学与应用物理(英文)
• 学科: 数学
• 关键词: FIELD Theory FIELD Unification General RELATIVITY Standard Model ELEMENTARY Particles
• 年，卷（期）: 2019,（6）
• 页码范围: 1304-1328
• 页数: 25页
• 分类号: O1

摘要

An alternative approach to the usual Kaluza-Klein way to field unification is presented which seems conceptually more satisfactory and elegant. The main idea is that of associating each fundamental interaction and matter field with a vector potential which is an eigenvector of the metric tensor of a multidimensional space-time manifold ?(n-dimensional “vierbein”). We deduce a system of field equations involving both Einstein and Maxwell-like equations for the fundamental fields. Confinement of the fields within the observable 4-dimensional space-time and non-vanishing particles’ rest mass problem are shown to be related to the choice of a scalar boson field (Higgs boson) appearing in the theory as a gauge function. Physical interpretation of the results, in order that all the known fundamental interactions may be included within the metric and connection, requires that the extended space-time is 16-dimensional. Fermions are shown to be included within the additional components of the vector potentials arising because of the increased dimensionality of space-time. A cosmological solution is also presented providing a possible explanation both to space-time flatness and to dark matter and dark energy as arising from the field components hidden within the extra space dimensions. Suggestions for gravity quantization are also examined.