Unified field theories

A collective name for the attempts to represent all or some physical fields (most often gravitational and electromagnetic fields) as manifestations of a single fundamental field, in the same way as the electric and magnetic fields are manifestations of the electromagnetic field. Unified field theories may be conventionally divided in two types: in the first, the field of some geometric object in the space of events forms the fundamental field (for example, the different versions of A. Einstein's unified field theories , and geometro-dynamics [2]); in the second, the fundamental field does not have a geometric nature (for example, non-linear spinor field theories). Some unified field theories have managed to produce successful estimates of fundamental physical constants.

Presently one has formulated in general terms a unified theory of the basic fields, excepting the gravitational field (the so-called Weinberg–Salam theory), and has sketched the outline of a unified theory including the gravitational field.

These theories use the most varied collection of methods and concepts from contemporary mathematics. In particular, the popular idea of T. Kaluza [3] and O. Klein [4] that space-time may have more than $4$ dimensions has been revived. The additional dimensions appear hardly ever in macrophysics, since they are twisted into ultra-small similar tori (the idea of compactification). By modern estimates [5], the dimension of such a space can be of the order of $50$ or larger.

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