Geometrization of the electromagnetic field and dark matter
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eometrization of the Electromagnetic Field and Dark Matter1 I. B. Pestov Bogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, Dubna, Moscow, 141980 Russia Abstract—Fundamental concepts, symmetries and dynamic equations of the theory of dark matter are derived from the simple relation: everything in the concept of space and the concept of space in everything. It is shown that the electromagnetic field is the singlet state of the dark matter field and, hence, the last may be considered as a generalized electromagnetic field (shortly gef) and a simple solution is given to the old problem of connecting the electromagnetic field with geometric properties of the physical manifold itself. It is shown that gauge fixing renders the generalized electromagnetic field effectively massive while the Maxwell electromagnetic field remains massless. To learn more about interactions between matter and dark matter on the microscopic level (and to recognize the fundamental role of internal symmetry in this case), the general covariant Dirac equation is derived and its natural generalization is considered. The experiment is suggested to test the formulated theory. DOI: 10.1134/S1063779613030106 1
1. INTRODUCTION
The problem of invisible mass is acknowledged to be among the greatest puzzles of modern cosmology and field theory (see, for example [1] and [2]). The most direct evidence for the existence of large quanti ties of dark matter in the Universe comes from the astronomical observation of the motion of visible mat ter in galaxies [3]. One neither knows the identity of the dark matter nor whether there is one or more types of its structure elements. The most commonly dis cussed theoretical elementary particle candidates are a massive neutrino, a sypersymmetric neutralino and the axion. So at the present time there is a good prob ability that the set of known fields is by no means lim ited to those fields. Moreover, we are free to look for deeper reasons for the existence of a new entity unusual in many respects. Of course, such reasoning is grounded on the point of view that there is a general and easily visible mathematical structure that stands behind all phenomena that we observe. We put forward an idea that a needed mathematical structure is defined by the fundamental relation: everything in the concept of manifold and the concept of manifold in everything. Here a field theory of the socalled dark matter is derived from the only first principle. Accord ing to the modern viewpoint, a fundamental physical theory is the one that possesses a mathematical repre sentation whose elements are a smooth manifold and geometrical objects defined on this manifold. Most physicists nowadays consider a theory be fundamental only if it does make explicit use of this concept. This picture is generally accepted and it is based on such a long history of physical research that there is no reason to question it. The geometrical structure of the physi 1 The article is published in the original.
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