Gauge and Lorentz transformation placed on the same foundation

TL;DR

This paper proposes a unified foundation for gauge and Lorentz transformations, leading to a new way of constructing interactions for arbitrary spin fields that preserves causality and correct high-energy behavior.

Contribution

It introduces a framework where gauge and Lorentz transformations are unified, enabling consistent non-minimal couplings for higher spin fields.

Findings

Causality is preserved for higher spin interactions.

Correct gyromagnetic ratio g=2 is achieved.

High-energy behavior of fields is improved.

Abstract

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.