Inertia II: The local induced inertia effects

Communications of the Byurakan Astrophysical Observatory Pub Date : 2024-01-09 DOI:10.52526/25792776-23.70.2-212

G. Ter-Kazarian

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Abstract

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.

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惯性 II：局部诱导惯性效应

局域MSp-SUSY理论是全局主空间（MSp）-SUSY理论的延伸（Ter-Kazarian，2023，2024），我们在局域MSp-SUSY理论的框架内讨论了加速运动和惯性效应。超空间是弯曲背景双空间 M4⊕MSp 的直接总和，其中包含了由旋子（θ, ¯Θ）诱导的额外费米子坐标（Θ, ¯Θ），而旋子（θ, ¯θ）是指向 MSp 的。我们把洛伦兹群作为我们的结构群，以恢复严格的超空间作为我们动力学理论的极限解决方案。局域MSp-SUSY被认为是一种量场理论，其作用包括虚构引力场项，其中引力子与拉里塔-斯克温格动力学项描述的所谓引力子（粒子）的非离子场共存。标准超引力理论与局域MSp-SUSY理论的重要区别在于，超引力与物质超场的耦合不再成立。我们认为，MSp的变形/（局部内部特性的扭曲）是绝对加速度（aabs=0）和惰性效应（虚构引力）的起源。这些引力场没有来源，是通过坐标变换产生的。这是指相关粒子本身，与其他物质场无关，因此可以通过适当的坐标变换在全球范围内消除。EA(z)中的超空间是卡坦局部框架的类似物，是超空间变换的动态变量，它标识了radfielde ˆ a ˆ m(X)和Rarita-Schwinger场。连接是这一理论中最重要的动力变量。e ˆ a ˆ m(X)场扮演着与局部变换（虚引力子）相关的量场的角色。虚构引力子是与局域超对称相关的量场。这两个量场的自旋不同：引力子为 2，引力子为 3/2。继特尔卡扎里安（TerKazarian，2012）之后，我们在经典物理学框架内讨论了惰性效应，超越了局域性假说，并得出了惰性双烯的显式形式：a ˆ m( )≡（ea m( )，e a m( )）。这一理论为引入弱等效原理（WPE）提供了合理解释，并给出了在黎曼-卡尔坦空间中运动的延伸旋转体所受相对论惯性力的一般表达式。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Communications of the Byurakan Astrophysical Observatory

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