Gauge fields and four interactions in the trigintaduonion spaces
- Zi-Hua Weng
Abstract
The paper aims to apply the trigintaduonion spaces to explore the
physical properties of four interactions simultaneously, including the
electromagnetic fields, gravitational fields, weak nuclear fields, and
strong nuclear fields. J. C. Maxwell first applied the algebra of
quaternions to study the physical properties of electromagnetic fields.
It inspired some subsequent scholars to introduce the quaternions,
octonions, sedenions, and trigintaduonions to research the
electromagnetic fields, gravitational fields, weak nuclear fields,
strong nuclear fields, quantum mechanics, gauge fields, and curved
spaces and so forth. The algebra of trigintaduonions is able to discuss
the physical quantities of four interactions, including the field
potential, field strong, field source, linear momentum, angular
momentum, torque, and force. In the field theories described with the
algebra of trigintaduonions, the weak nuclear field is composed of three
types of fundamental fields. These three fundamental fields, related to
weak nuclear fields, can describe the physical properties of weak
nuclear fields collectively. This is consistent with the conclusion of
the electroweak theory. Meanwhile the strong nuclear field consists of
three types of fundamental fields. These three fundamental fields
relevant to strong nuclear fields may investigate the physical
properties of strong nuclear fields mutually. It is coincident with the
deduction of quark theory. According to the properties of
trigintaduonions, one can deduce the Yang-Mills equation related to the
gauge fields. It means that the electromagnetic field occupies a
quaternion space. The gravitational field owns one different quaternion
space. The weak nuclear fields occupy three mutually independent
quaternion spaces. The properties of weak nuclear fields are different
from those of electromagnetic fields or gravitational fields. According
to the multiplicative closure, the strong nuclear fields also own three
quaternion spaces independent of each other. These explorations further
deepen the understanding of the physical properties of weak and strong
nuclear fields.20 Feb 2024Submission Checks Completed 20 Feb 2024Assigned to Editor
29 Feb 2024Review(s) Completed, Editorial Evaluation Pending
15 Mar 2024Reviewer(s) Assigned
28 Jun 2024Review(s) Completed, Editorial Evaluation Pending