View source for 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|geometro-dynamics]] [[#References|[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 [[#References|[3]]] and O. Klein [[#References|[4]]] that space-time may have more than <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/u/u095/u095180/u0951801.png" /> 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 [[#References|[5]]], the dimension of such a space can be of the order of <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/u/u095/u095180/u0951802.png" /> or larger.

====References====
<table><TR><TD valign="top">[1a]</TD> <TD valign="top">  A. Einstein,   W. Mayer,   ''Sitzungsber. Preuss. Akad. Wissenschaft. Phys.-Math. Kl.''  (1931)  pp. 541–547</TD></TR><TR><TD valign="top">[1b]</TD> <TD valign="top">  A. Einstein,   W. Mayer,   ''Sitzungsber. Preuss. Akad. Wissenschaft. Phys.-Math. Kl.''  (1932)  pp. 130–137</TD></TR><TR><TD valign="top">[2]</TD> <TD valign="top">  J.A. Wheeler,   "Geometrodynamics" , Acad. Press  (1962)</TD></TR><TR><TD valign="top">[3]</TD> <TD valign="top">  T. Kaluza,   ''Sitzungsber. Preuss. Akad. Wissenschaft. Phys.-Math. Kl.''  (1921)  pp. 966</TD></TR><TR><TD valign="top">[4]</TD> <TD valign="top">  O. Klein,   ''Z. Physik'' , '''37'''  (1926)  pp. 895–906</TD></TR><TR><TD valign="top">[5]</TD> <TD valign="top">  E. Cremmer,   B. Julia,   J. Scherk,   ''Phys. Letters B'' , '''76'''  (1978)  pp. 409</TD></TR></table>



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====References====
<table><TR><TD valign="top">[a1a]</TD> <TD valign="top">  A. Einstein,   ''Sitzungsber. Preuss. Akad. Wissenschaft. Phys.-Math. Kl.''  (1927)  pp. 23–30</TD></TR><TR><TD valign="top">[a1b]</TD> <TD valign="top">  A. Einstein,   P. Bergmann,   "On a generalization of Kaluza's theory of electricity"  ''Ann. of Math. (2)'' , '''40'''  (1938)  pp. 683–701</TD></TR><TR><TD valign="top">[a2]</TD> <TD valign="top">  W. Heisenberg,   "The nonlinear theory of elementary particles" , Univ. Rochester  (1960)</TD></TR><TR><TD valign="top">[a3]</TD> <TD valign="top">  T. Appelquist,   A. Chodos,   P.G.O. Freund,   "Modern Kaluza–Klein theories" , Addison-Wesley  (1987)</TD></TR></table>