/ 04 07 05 7 v 4 1 0 O ct 2 00 4 Natural beauty of the standard model - A derivation of the electro - weak unified and quantum - gravity theory without assuming a Higgs particle

We study the asymptotic behavior of a singular potential that arises under several frequently occurring analytic behaviors of the eigen functions (of the Schrödinger eigenvalue problem) without introducing cut-offs. Instead, in our analyses we focus on power behaviors of eigen functions. We find that the asymptotic behavior of the singular potential crucially depends on the analytic property of the eigen functions near the singular point. Then, we discuss the self-consistency condition for the spherical symmetric Klein-Gordon equation, and discuss a natural possibility that gravity and weak coupling constants gG and gW may be defined after gEM . In this point of view, gravity and the weak force are subsidiary derived from electricity. Particularly, SU(2)L×U(1) unification is derived without assuming a phase transition. A possible origin of the Higgs mechanism is proposed. Each particle pair of the standard model is associated with the corresponding asymptotic expansion of an eigen function. Next we consider the meaning of internal and external degrees of freedom for a 2 body problem, and find two degrees of freedom which can not reduce to the local motion of one frame. These two degrees of freedom are inherent to the Poincaré group. These two scalars can be expressed in terms of an asymmetric spinor representation, and regarded as the origin of a complex U(1) phase. Then we try to 1This thesis was, however, rejected by the judging committee, without even mentioning sections 4-7. They forced me to omit sections 3-7 at all. Thus, only the revised version of Section 2 was approved by the judging committee.