A Possible Origin of Dynamical Gauge Field

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Our achievements under the support of this Grant are summarized as follows.(1) Induced gauge theoryIn most of theories which try to unify the particle interactions, one usually assumes a high gauge symmetries in an extremely high energy region, then one introduces a spontaneous symmetry breakdown to get the standard theory. In this project we found a new mechanism that even if a theory has a low gauge symmetry in high energy region, some higher gauge symmetry is able to be induced in low energy region. This is nicely realized in connection with the Kaluza-Klein compactification of the space and the Berry phase effect.We started off from a model of the gravity and U (1) -gauge field A_M, (M=0,1,2, ・・・, 5) interacting with a fermion field in 6-dimensions. If one assumes that the space is compactified into a 4-dimensional Minkowski space times a 2-dimensional Riemann surface with genus G,then ordinary Kaluza-Klein theory tells us that one U (1) -gauge field A_M, (M=0,1, ・・・, 3), two Kaluz … More a-Klein U (1) -gauge fields comming from the metric tensor, and 4 scalar fields are expected to come out in 4-dimensional space. We have demonstrated that if the compactified spece is topologically non-trivial such as the Riemann surface with genus G>0, then the holonomy fields generate a set of new composite gauge fields. The degrees of freedom of the induced gauge fields come from the holonomies, and the holonomies are composite fields of the compactified space dimensional components of the U (1) -gauge field which is originally prepared in the model.(2) A miniature model of multi universesTo understand a possible theory of everything, we have studied a miniature model generating multi universes. This is an ordinary string model, but we assume that a connected piece of string represents a 1+1 dimensional universe. The universe, when scattered by other universe, splits up into two or many universes. We have confirmed, when the universe is gigantic, it is quite stable especially around the center of the universe. This implies that the emission of micro-universes occurs at the edge of it. On the universe, however, no low energy matter fields are found. All the local excitation in the universe are of the order of the Planck energy. Having analyzed this model we have found a possibility that our space-time and the matter field degrees of freedom are all on a same footing, so that the space and the matter are able to be unified in a single theory. Less