Vector fields on C*-algebras, semigroups of endomorphisms and gauge groups

TL;DR

This paper explores the concept of vector fields on C*-algebras, their connection to semigroups of endomorphisms, and includes constructions with potential physical interpretations, laying groundwork for future research.

Contribution

It defines vector fields on C*-algebras and investigates their relationship with semigroups of endomorphisms, introducing new constructions including a Minkowski space parametrization.

Findings

Established a definition for vector fields on C*-algebras

Analyzed the relation between vector fields and semigroups of endomorphisms

Presented a construction of semigroups parametrized by Minkowski space cone

Abstract

What is a vector field on a C*-algebra is defined. Its relation to semigroups of endomorphisms was researched. Some results given about those vector fields and semigroups. There are also various constructions of semigroups including one parametrized by the cone of the future in (3+1)-dimensional Minkowski space. Physical interpretations will be presented in a separate paper.