Jauge discontinue et particules dans un hyperespace-temps multiconnexe

Quantization of gauge fields through fibre bundle multiconnectivity

“…If one has in mind the construction of a geometric unified field theory of the Kaluza-Klein type, the application of the above method of quantization requires a hyperspace-time having at least five dimensions. By analogy with [3], we shall suppose that the space added to space-time, called the superior space, has a positive constant curvature and is of odd dimension. The simplest superior space is then S 1 (κ), i.e.…”

“…This paper is based on [2]. It is also an extension, with some corrections, of [3] where the quantification of non-gravitational interaction fields was explained through the geometry of a hyperspace-time of the Kaluza-Klein type. The discrete nature of these interaction fields was then motivated by the multiconnectivity of the space added to space-time and which was called superior space.…”

“…More precisely, the discretization was related to the monodromy group of the superior space seen as a covering space. This discrete group leads to the introduction of the notion of discrete gauge, some properties of which are given in [3]. After we have extended the geometric framework of the preceding work, we shall investigate more deeply the notions of discrete gauge and discontinuous fibre bundle.…”

Discretization and Interaction of Fields via the Classical Kaluza-Klein Theory

“…A more complete geometric modeling of electromagnetism must also allow expressing the discontinuity of certain functions associated with an electrically charged particle, such as its energy when it is involved in an interaction. To model this discontinuous variation, we shall postulate that the geometric structure of the fifth dimension has a global symmetry making it multiconnected [3][4][5]. The fifth dimension then decomposes into equal length intervals, each topologically equivalent to the circle S…”