The Master-Space Supergravity: Particle mechanics

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.