Harmonic analysis of spacetime with hypercharge and isospin
Abstract
In analogy to the harmonic analysis for the Poincar\'e group with its irreducible representations characterizing free particles, the harmonic analysis for a nonlinear spacetime model as homogenous space of the extended Lorentz group GL(C2) is given. What the Dirac energy-momentum measures are for free particles, are multipole measures in the analysis of nonlinear spacetime - they are related to spacetime interactions. The representations induced from the nonlinear spacetime fixgroup U(2) connect representations of external (spacetimelike) degrees of freedom with those of internal (hypercharge-isospinlike) ones as seen in the standard model of electroweak and strong interactions. The methods used are introduced and exemplified with the nonrelativistic Kepler dynamics in an interpretation as harmonic analysis of time and position functions.
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