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.

References

[1a]	A. Einstein, W. Mayer, Sitzungsber. Preuss. Akad. Wissenschaft. Phys.-Math. Kl. (1931) pp. 541–547
[1b]	A. Einstein, W. Mayer, Sitzungsber. Preuss. Akad. Wissenschaft. Phys.-Math. Kl. (1932) pp. 130–137
[2]	J.A. Wheeler, "Geometrodynamics" , Acad. Press (1962)
[3]	T. Kaluza, Sitzungsber. Preuss. Akad. Wissenschaft. Phys.-Math. Kl. (1921) pp. 966
[4]	O. Klein, Z. Physik , 37 (1926) pp. 895–906
[5]	E. Cremmer, B. Julia, J. Scherk, Phys. Letters B , 76 (1978) pp. 409

References

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