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Gauge and Lorentz transformation placed on the same foundation. (English) Zbl 1238.81139

Summary: 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. As a consequence, on this stage the (electromagnetic) 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.

MSC:

81R20 Covariant wave equations in quantum theory, relativistic quantum mechanics
70S15 Yang-Mills and other gauge theories in mechanics of particles and systems
81R05 Finite-dimensional groups and algebras motivated by physics and their representations
81T13 Yang-Mills and other gauge theories in quantum field theory
22E70 Applications of Lie groups to the sciences; explicit representations
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