Abstract
A quantized geometrical description of hadron extension is developed based on Drechsler's soldered de Sitter fiber bundle, which possesses as fiber a local four-dimensional Riemannian space of constant curvature characterized by a radius of curvatureR of the order of 1 Fermi. The structural (gauge) group of the bundle is a de Sitter SO(4, 1), which contains all observable transformations (rotations as well as translations). The quantized de Sitter-structured connection of the bundle leads to a set of self-interaction gauge operators that “act back” on the de Sitter bundle by inducing a local curvature, which, in turn, affects a small neighborhood of the adjoining space-time position, leading to the experimentally observed “size” of the hadron. A particular choice for the quantized Lorentz cross section (gauge) is made that leads to the mathematically consistent and experimentally verifiable hadron model, the quantum relativistic rotator. Also investigated is the limit corresponding to taking the radius of curvature of the de Sitter fiber to infinity.
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Aldinger, R.R. Quantum de Sitter fiber bundle interpretation of hadron extension. Int J Theor Phys 25, 527–544 (1986). https://doi.org/10.1007/BF00668787
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DOI: https://doi.org/10.1007/BF00668787