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Teleparallel Supergravity ; Spacetime Deformation ; Inertia Effects
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This is the first of three articles that explore the possibility of quantum mechanical inertial properties of the Dirac particle beyond the `hypothesis of locality´. This is done within the framework of the Master Space-Teleparallel Supergravity (MS gp-TSG) (Ter-Kazarian, 2025) theory, which we recently proposed to account for inertial effects (Ter-Kazarian, 2026). The `hypothesis of locality´ used for extension of the Lorentz invariance to accelerated observers within the Special Relativity. This hypothesis in effect bypasses acceleration and replaces the accelerated observer by a continuous infinity of hypothetical momentarily comoving inertial observers along its wordline. Despite the successes for the tiny accelerations we usually experience, when the curvature of the wordline could be ignored and that the differences between observations by accelerated and comoving inertial observers will also be very small, however, the basic conceptual framework of this assumption has been considered by many scientists to be unsatisfactory. In general case, this is actually untenable and represents strict restrictions, and that the hypothesis of locality will have to be extended to describe physics for arbitrarily accelerated observers. This immediately leads to the disturbing fact within the MS gp-TSG theory that the metric of a twodimensional semi-Riemannian space, calculated in the non-inertial frame of reference of an accelerating and rotating observer, becomes incomplete. To recover the complete metric, therefore, our strategy in the latest paper (Ter-Kazarian, 2026) was to go beyond this hypothesis by invoking a general deformation of the flat master space, MSp → MS gp. Continuing along this line, in present article, we compute the object of anholonomicity and connection defined with respect to the anholonomic frame. Based on these premises, we derive the explicit form of the Dirac equation for an observer in a reference frame that is accelerated and rotating.