A new framework for the unification of fundamental physics - Affine connection representation of gauge fields

Zhao-Hui MAN
2021 Zenodo  
There are two ways to unify gravitational field and gauge field. One is to represent gravitational field as principal bundle connection, and the other is to represent gauge field as affine connection. Poincare gauge theory and metric-affine gauge theory adopt the first approach. This paper adopts the second. An affine connection is used to establish a unified coordinate description of gauge field and gravitational field. This theory has the following advantages. (i) Gauge field and
more » ... field can both be represented by affine connection; they can be described by a unified spatial frame. (ii) Time can be regarded as the total metric with respect to all dimensions of internal coordinate space and external coordinate space. On-shell can be regarded as gradient direction. Quantum theory can be regarded as a geometric theory of distribution of gradient directions. Hence, gravitational theory and quantum theory obtain the same view of time and space and a unified description of evolution in affine connection representation of gauge fields. (iii) Chiral asymmetry, coupling constants, MNS mixing and CKM mixing can appear spontaneously as geometric properties in affine connection representation, whereas in $U(1) \times SU(2)\times SU(3)$ principal bundle connection representation they can just only be artificially set up. Some principles and postulates of conventional theories can be turned into theorems in affine connection representation, so they are not necessary to be regarded as principles or postulates anymore. (iv) The unification theory of gauge fields that are represented by affine connection can avoid the problem that a proton decays into a lepton. (v) Since the concept of point particle is thoroughly abandoned, this theory is not required to be renormalized. The Standard Model is not possessed of the above advantages. In the affine connection representation, we can get a better interpretation of these physical properties. This is probably a necessary step towards the ultimate theory of physics.
doi:10.5281/zenodo.4706193 fatcat:isnwjn5xgffptbaivdvpbgqynu