Gauge and Lorentz transformation placed on the same foundation

Details Gauge and Lorentz transformation placed on the same foundation Gauge and Lorentz transformation placed on the same foundation

2010-06-10

arxiv.org/abs/1006.2039v2

Adv. Math. Phys.2011:652126, 2011

Physics

High Energy Physics

High Energy Physics - Theory

12 pages, no figures, published version. arXiv admin note: substantial text overlap with arXiv:0908.3761

Scientific paper

10.1155/2011/652126

In this note we show that a "dynamical" interaction for arbitrary spin can be constructed in a straightforward way if gauge and Lorentz transformations are placed on the same foundation. As Lorentz transformations act on space-time coordinates, gauge transformations are applied to the gauge field. Placing these two transformations on the same ground means that all quantized field like spin-1/2 and spin-3/2 spinors are functions not only of the coordinates but also of the gauge field components. This change of perspective solves a couple of problems occuring for higher spin fields like the loss of causality, bad high-energy properties and the deviation of the gyromagnetic ratio from its constant value g=2 for any spin, as caused by applying the minimal coupling. Starting with a "dynamical" interaction, a non-minimal coupling can be derived which is consistent with causality, the expectation for the gyromagnetic ratio, and well-behaved for high energies. As a consequence, on this stage the (elektromagnetic) gauge field has to be considered as classical field. Therefore, standard quantum field theory cannot be applied. Despite this inconvenience, such a common ground is consistent with an old dream of physicists almost a century ago. Our approach, therefore, indicates a straightforward way to realize this dream.

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