Gauge theory and little gauge theory

TL;DR

This paper reexamines gauge theory through geometric vector space concepts, introduces 'little gauge theory' to restrict connection forms, and explores its implications for Cartan geometry, fermion fields, and Higgs bosons.

Contribution

It introduces the novel concept of 'little gauge theory' that constrains connection fields and extends existing theories including Dirac fermions and Higgs fields.

Findings

'Little gauge theory' restricts connection forms.

Extension of Sogami's covariant derivative for fermions.

Higgs bosons are incorporated into new fields.

Abstract

The gauge theory is the most important type of the field theory, in which the interactions of the elementary particles are described by the exchange of the gauge bosons.In this article, the gauge theory is reexamined as geometry of the vector space, and a new concept of "little gauge theory" is introduced. A key peculiarity of the little gauge theory is that the theory is able to give a restriction for form of the connection field. Based on the little gauge theory, Cartan geometry, a charged boson and the Dirac fermion field theory are investigated. In particular, the Dirac fermion field theory leads to an extension of Sogami's covariant derivative. And it is interpreted that Higgs bosons are included in new fields introduced in this article.