Gauge and Lorentz Transformation Placed on the Same Foundation

Abstract EN

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.