Article citationsMore>>

Gürsey, F. (1964) Introduction to Group Theory. In: DeWitt, C. and DeWitt, B., Eds., Relativity, Groups and Topology, Gordon and Breach Science Publishers, New York, 89-161.

has been cited by the following article:

• TITLE: Mathematical Aspects of SU (2) and SO(3,R) Derived from Two-Mode Realization in Coordinate-Invariant Form

  AUTHORS: Alfred Wünsche

  KEYWORDS: Boson Operators, Lie Algebra, Root Diagram, Invariant Integration, Hamilton-Cayley Identity, Cayley-Gibbs-Fyodorov Parametrization, Composition Law, Quaternion, Stereographic Projection, Fractional Linear Transformation

  JOURNAL NAME: Journal of Modern Physics, Vol.14 No.3, February 28, 2023

  ABSTRACT: Some mathematical aspects of the Lie groups SU (2) and in realization by two pairs of boson annihilation and creation operators and in the parametrization by the vector parameter instead of the Euler angles and the vector parameter c of Fyodorov are developed. The one-dimensional root scheme of SU (2) is embedded in two-dimensional root schemes of some higher Lie groups, in particular, in inhomogeneous Lie groups and is represented in text and figures. The two-dimensional fundamental representation of SU (2) is calculated and from it the composition law for the product of two transformations and the most important decompositions of general transformations in special ones are derived. Then the transition from representation of SU (2) to of is made where in addition to the parametrization by vector the convenient parametrization by vector c is considered and the connections are established. The measures for invariant integration are derived for and for SU (2) . The relations between 3D-rotations of a unit sphere to fractional linear transformations of a plane by stereographic projection are discussed. All derivations and representations are tried to make in coordinate-invariant way.