Abstract
Dirac field equations are studied for spinor fields without any external interaction and when they are considered on a background having a tensorial connection with a specific non-vanishing structure some solution can be found in polar form displaying a square-integrable localized behaviour.
Highlights
Physics as seen from a very general perspective consists in writing a system of field equations and finding the corresponding solutions
Dirac field equations are studied for spinor fields without any external interaction and when they are considered on a background having a tensorial connection with a specific non-vanishing structure some solution can be found in polar form displaying a square-integrable localized behaviour
The square-integrability of the polar solution is a direct consequence of the existence of the negative energy contribution, that is of the existence of the covariant attractive inertial force given as tensorial connection, for the free Dirac differential field equation
Summary
Physics as seen from a very general perspective consists in writing a system of field equations and finding the corresponding solutions Once found, these solutions are applied to particular cases so to make specific predictions that are later compared to experiments and observations. By taking considerable advantage of the methods that we have drawn in references [9,10,11], some solutions, explicit, square-integrable and completely self-sustained, could be obtained. This is what we will be showing in this work
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