Inertia II: The local induced inertia effects

This report aims to expose further the assertions made in a recent theory of global Master space (MSp)-SUSY (Ter-Kazarian, 2023a, 2024a) by developing its local extension. The global MSp-SUSY reviews the physical processes underlying the standard Lorenz code of motion and its deformation tested in experiments for ultra-high energy cosmic ray and TeV-γ photons observed. The local extension of MSp-SUSY yields the gauge theory of translations. This as a corollary makes room for the theory of MS gpSupergravity, subject to certain rules. The superspace is a direct sum of background semi-Riemannian 4D-space and curved Master space MS gp ≡ V 2 (2D semi-Riemannian space), V4 ⊕ V 2 , with an inclusion of additional fermionic coordinates Θ(θ, ¯θ) and Θ( ¯ θ, ¯θ), which are induced by the spinors θ and ¯θ referred to MS gp. Being embedded in V4, the MS gp is the unmanifested indispensable individual companion of a particle of interest devoid of any matter influence. While all the particles are living on V4, their superpartners can be viewed as living on MS gp. In this framework supersymmetry and general coordinate transformations are described in a unified way as certain diffeomorphisms. The action of simple MS gp-SG includes the Hilbert term for a fictitious graviton (with spin 2) coexisting with a fictitious fermionic field of, so-called, gravitino (sparticle with spin 3/2) described by the Rarita-Scwinger kinetic term. They are the bosonic and fermionic states of a gauge particle in V4 and MS gp, respectively, or vice versa. A curvature of MS gp arises entirely due to the inertial properties of the Lorentz-rotated frame of interest. This refers to the particle of interest itself, without relation to other matter fields, so that this can be globally removed by appropriate coordinate transformations. The supervielbein, being an alogue of Cartan’s local frame, is the dynamical variable of superspace formulation, which identifies the tetrad field and the Rarita-Schwinger fields. The spin connection is the second dynamical variable in this theory. The tetrad field plays the role of a gauge field (graviton) associated with local transformations. The gravitino is a gauge field associated with local supersymmetry. Within that context, we consider particle mechanics.

The Master-Space Supergravity: Particle mechanics

Ter-Kazarian

2024

The Master-Space Teleparallel Supergravity: Accelerated frames

Ter-Kazarian

2024

Using Palatini’s formalism extended in a plausible fashion to the recent MS gp-Supergravity (TerKazarian, 2023c, 2024b), subject to certain rules, we reinterpret a flat MS gp-SG theory with Weitzenb¨ock torsion as the quantum field theory of Master-Space Teleparallel Supergravity (MS gp-TSG), having the gauge translation group in tangent bundle. Here the spin connection represents only inertial effects, but not gravitation at all. In order to recover the covariance, we introduce a 1-form of the Yang–Mills connection assuming values in the Lie algebra of the translation group. The Hilbert action vanishes and the gravitino action loses its spin connections, so that the accelerated reference frame has Weitzenb¨ock torsion induced by gravitinos. Due to the soldered character of the tangent bundle, torsion presents also the anholonomy of the translational covariant derivative. The gauge invariance of the tetrad provides torsion invariance under gauge transformations. The role of the Cartan-Killing metric usually comes, when it exists, from its being invariant under the group action. Here it does not exist, but we use the invariant Lorentz metric of Minkowski spacetime in its stead. The action of MS gp-TSG is invariant under local translations, under local super symmetry transformations and by construction is invariant under local Lorentz rotations and under diffeomorphisms. So that this action is invariant under the Poincar´e supergroup and under diffeomorphisms. We show the equivalence of the Teleparallel Gravity action with Hilbert action, which proves that the immediate cause of the fictitious Riemann curvature for the LeviCivita connection arises entirely due to the inertial properties of the Lorentz-rotated frame of interest. The curvature of Weitzenb¨ock connection vanishes identically, but for a tetrad involving a non-trivial translational gauge potential, the torsion is non-vanishing. We consider Weitzenb¨ock connection a kind of dual of the Levi-Civita connection, which is a connection with vanishing torsion, and non-vanishing fictitious curvature. The Weitzenb¨ock connection defines the acceleration through force equation, with torsion (or contortion) playing the role of force.

A deformation of Master-Space and inertia effects within the theory of Master Space-Teleparallel Supergravity

Ter-Kazarian

2024

In the framework of the theory of Master space-Teleparallel Supergravity (MS gp-TSG) (Ter-Kazarian, 2024b), having the gauge translation group in tangent bundle, in present article we address the theory of a general deformation of the flat MSp induced by external force exerted on a particle, subject to certain rules. Our idea is that the universality of gravitation and inertia attribute to the single mechanism of origin from geometry but having a different nature.