Compactification (physics)

In Kaluza-Klein compactification ( also briefly compactification if no likelihood of confusion with the mathematical term is ) is understood in theoretical physics, the reduction of a higher dimensional theory on a niedrigerdimensionale.

The name goes back to the Kaluza - Klein theory, in which resulting from a five-dimensional theory, both the four-dimensional Einstein field equations and the Maxwell equations. The term is also used in particular in the reduction of the 26 -dimensional bosonic or the 10 -dimensional supersymmetric string theory on a four-dimensional effective theory or in the reduction of 11 -dimensional supergravity on a 10 -dimensional theory.

In the Kaluza-Klein compactification at first the extra dimensions are compactified by complement of a point in the topological sense, for example. Thereafter, this compact dimensions are " shrunk " so that they reach the scale of the Planck length. The resulting effective theory takes of these dimensions then only turns true.

String theory

In string theory, one speaks of compactified or rolled-up dimensions. By this is meant that the topological structure of a dimension loop, ie, a is. A two-dimensional space with a compact dimension would be as it were an infinitely long cylinder, represented mathematically as. Similarly, one must in the ( supersymmetric ) string theory imagine spacetime as a kind of 10 -dimensional cylinder, are of the 6 dimensions as a circle.

Although the mathematical compactification with a point at infinity suggests that this dimension is very large. The correct view is that the scope of such a dimension is to be sought rather in the field of the Planck length. As with the mathematical compactification is achieved by revolving the compact dimension again the same point. This mathematical background leads to the philosophical way of speaking of rolling up the dimensions into a circle.