Difference between revisions of "Unified field theories"
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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. | 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. | 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 | + | 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 $4$ 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 [[#References|[5]]], the dimension of such a space can be of the order of $50$ or larger. |
====References==== | ====References==== | ||
Latest revision as of 16:53, 2 July 2014
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 |
Comments
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) |
Unified field theories. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Unified_field_theories&oldid=32351