2007/12/14 by John Fredsted, Fredsted, John
Computer Science · Mathematics · Physics and Astronomy · #Computational Physics and Python Applications #Cosmology and Gravitation Theories #math-ph #math.MP #msc:17A75 #msc:22E60 #msc:70S15
paper · pdf · doi:10.48550/arxiv.0712.2435
7 pages, LaTeX; typos corrected
arxiv created 2007/12/15 · arxiv updated 2009/12/01
Using complexified quaternions, an intriguing link between generators of two different and surprisingly commuting four-dimensional representations of the SU(2)xU(1) Lie group, and generators of two four-dimensional spin 1/2 representations of the Spin(3,1) Lie group is established: the former generators completely determine the latter ones, and cross-combined they constitute two different, but closely related, four-dimensional representations of Spin(3,1)xSU(2)xU(1). These representations are used to construct a Spin(3,1)xSU(2)xU(1) gauge invariant Lagrangian, containing two four-spinors consisting not as usual of Weyl two-spinors of opposite helicity and equal weak isospin, but instead of Weyl two-spinors of opposite weak isospin and equal helicity, a construction which arises naturally from the mathematical formalism itself. A possible future generalization, using complexified octonions, is discussed.