Kaluza Klein Particle

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Kaluza-Klein particles are hypothetical elementary particles that are postulated by the Randall-Sundrum model with the aid of the Kaluza-Klein theory .

The Kaluza-Klein theory and its application in string theory

The Kaluza-Klein theory is a five-dimensional field theory and was first formulated by Theodor Kaluza . It represents one of the first unified theories in that it postulates a five-dimensional spacetime , where Maxwell's equations from electrodynamics and the field equations from general relativity can be applied simultaneously.

Oskar Klein expanded this idea by assuming that the additional fifth dimension was compacted so that it could not be observed. This would quantize the charges. However, this theory fell into oblivion shortly after it was formulated.

This idea was later taken up by string theory, which also assumes compactified extra dimensions.

The Randall Sundrum Model

The Randall-Sundrum model also represents an attempt at great unification by considering spacetime as an anti-de-sitter space, which is thus negatively curved. In this model, two 4-branes are described, which are coded at the edge of a five-dimensional bulk . The gauge bosons of the three previously quantized interactions (electromagnetism, strong interaction, weak interaction) would be limited to one bran , while the graviton can move freely in the bulk. This model would explain why the gravitational force appears to be so weak.

The elementary particles are a "side effect" of this theory, since they must appear there. Very little is known about the structure of these particles themselves, other than that it originated in higher dimensions and is a four-dimensional particle.

literature

  • Thomas Appelquist: Modern Kaluza-Klein theories. Addison-Wesley, Redwood City 1987, ISBN 0-201-09829-6
  • Robert Coquereaux, Arkadiusz Jadcyzk: Riemannian geometry, fiber bundles, Kaluza-Klein theories and all that… . World Scientific, Singapore 1988, ISBN 9971-5-0426-X .
  • Paul S. Wesson: Five-dimensional physics - classical and quantum consequences of Kaluza-Klein cosmology. World Scientific, Singapore 2006, ISBN 978-981-256-661-4 .
  • M. Blau, W. Thirring, G. Landi: Introduction to Kaluza-Klein Theory. XXV. Int. University weeks for nuclear physics, Schladming / Austria, 19. – 27. February 1986, doi: 10.1007 / 978-3-642-71760-4 1 . Also in: Selected papers of Walter E. Thirring. Pp. 633-663, American Mathematical Soc., Providence 1998, ISBN 0-8218-0812-5 .
  • MJ Duff: Kaluza-Klein Theory in Perspective . Oskar Klein Centenary Nobel Symposium, Stockholm, 19. – 21. September 1994, arxiv : hep-th / 9410046 .
  • Hubert FM Goenner: On the History of Unified Field Theories . Living Rev. Relativity 7, 2004, doi: 10.12942 / lrr-2004-2 .
  • Albert Einstein: Th. Kaluza, on the unity problem of physics . Submitted to the Prussian Academy of Sciences, December 8, 1921 ( online ).