Representations of lie groups with applications to high energy physics

Abstract

This thesis is mainly concerned with that part of the theory of Lie groups needed to describe the symmetry principles used in the theory of strongly interacting particles. A Lie group is a group whose elements depend analytically on a number of continuously varying parameters. These groups are named after the Norwegian Mathematician Sophius Lie, who founded a general theory of such groups by considering their behaviour in the neighbourhood of the identity. His results were published in 1893 S.Lie and F.Engels, Theorie der transformationgruppen (Leipzig., 1893). A year later in 1894 E.Cartan published his thesis in which he proved the fundamental propositions concerning the structure and representations of Lie groups. This thesis was based on the work of Killing, who in the years 1888 - 1890 published a number of incomplete proofs on the subject. In the years 1896 - 1903 Frobenius created the theory of representation of groups by linear transformations. His work made extensive use of the character of a matrix. W.Burnside and later I.Schur created a simpler approach to the subject.