More on the Mathematics of the DLF Theory: Embedding of the Oscillator World L into Segal’s Compact Cosmos D

Abstract

The DLF theory can be understood as an attempt to modify the Standard Model by flexing the Poincare symmetry to certain 7-dimensional symmetries. The D part of the theory is known as Segal’s Chronometry which is based on compact cosmos D=U(2) with the SU(2,2) fractional linear action on it. The oscillator group is viewed as a subgroup LG of the conformal group G=SU(2,2) and certain LG-orbits L in D are studied. We prove existence of such L and of such an embedding of F=U(1,1) into D, that D differs from F by a certain torus whereas D differs from L by a circle on that torus. In the general U(p,q) vs U(p+q) case, the Sviderskiy formula is described - as a tribute to the late Oleg S. Sviderskiy (July 31 1969 – March 30 2011).