Inertia II: The local induced inertia effects

Inthe frameworkof localMSp-SUSYtheory,which is extensionof global, socalled,master space (MSp)-SUSYtheory(Ter-Kazarian, 2023, 2024),weaddress theacceleratedmotionand inertiaeffects. The superspace isadirect sumof curvedbackgrounddouble spacesM4⊕MSp,withan inclusionof additional fermioniccoordinates(Θ, ¯ Θ) inducedbythespinors(θ,¯ θ),whichrefertoMSp.Wetakethe Lorentzgroupasour structuregroupinorder torecover rigidsuperspaceasa limitingsolutiontoour dynamicaltheory.ThelocalMSp-SUSYisconceivedasaquantumfieldtheorywhoseactionincludesthe fictitiousgravitationfieldterm,wherethegravitoncoexistswithafermionicfieldof, so-called,gravitino (sparticle) describedby theRarita-Scwinger kinetic term. Asignificant differencebetween standard theoriesof supergravityandthelocalMSp-SUSYtheoryisthatacouplingof supergravitywithmatter superfields no longer holds. We argue that adeformation/(distortionof local internal properties) of MSp, istheoriginof theabsoluteacceleration(aabs=0)andinertiaeffects(fictitiousgraviton). These gravitational fieldshadnosourcesandweregeneratedbycoordinate transformations. Acurvatureof MSparisesentirelyduetotheinertialpropertiesoftheLorentz-rotatedframeof interest.Thisrefersto theparticleof interestitself,withoutrelationtoothermatterfields,sothatthiscanbegloballyremoved byappropriatecoordinatetransformations. ThesupervielbeinEA(z),beinganalogueofCartan’s local frame, isthedynamicalvariableof superspaceformulation,whichidentifiesthetetradfielde ˆ a ˆ m(X)and theRarita-Schwingerfields. Theconnectionis theseconddynamicalvariable inthis theory. Thefield e ˆ a ˆ m(X)plays the roleof agaugefieldassociatedwith local transformations (fictitious graviton). The fictitiousgravitinoisthegaugefieldrelatedtolocalsupersymmetry.Thetwofieldsdifferintheirspin: 2 forthegraviton,3/2forthegravitino.Thesetwoparticlesarethetwobosonicandfermionicstatesofa gaugeparticleinthecurvedbackgroundspacesM4andMSp,respectively,orviceversa.Following(TerKazarian, 2012), inthe frameworkof classical physics,wediscuss the inertiaeffectsbygoingbeyond thehypothesisof locality, andderive theexplicit formof thevierbiene ˆ a ˆ m( )≡(ea m( ),e a m( )). This theoryfurnishesjustificationfortheintroductionoftheweakprincipleofequivalence(WPE).Wederive ageneralexpressionoftherelativisticinertial forceexertedontheextendedspinningbodymovinginthe Rieman-Cartanspace.