Fundamental Physics at the Vigier Centenary最新文献_第2页

The Dirac Electron Hypertube Revisited Nonlocal Parameters Within Extended Particle Elements 狄拉克电子超管对扩展粒子元非局域参数的重述

Fundamental Physics at the Vigier Centenary Pub Date : 2020-04-01 DOI: 10.1142/9789811246463_0001

R. Amoroso, J. Vigier

引用次数: 4

Of the Exterior Calculus and Relativistic Quantum Mechanics 外部微积分和相对论量子力学

Fundamental Physics at the Vigier Centenary Pub Date : 2019-01-23 DOI: 10.1142/9789811246463_0014

J. G. Vargas

{"title":"Of the Exterior Calculus and Relativistic Quantum Mechanics","authors":"J. G. Vargas","doi":"10.1142/9789811246463_0014","DOIUrl":"https://doi.org/10.1142/9789811246463_0014","url":null,"abstract":"In 1960-62, E. K\"ahler developed what looks as a generalization of the exterior calculus, which he based on Clifford rather than exterior algebra. The role of the exterior derivative, $du$, was taken by the more comprehensive derivative $partial u$ ($equiv dx^{mu }vee d_{mu }u$), where `$vee $' stands for Clifford product. The $d_{mu }u$ represents a set of quantities to which he referred as covariant derivative, and for which he gave a long, ad hoc expression. We provide the geometric foundation for this derivative, based on Cartan's treatment of the structure of a Riemannian differentiable manifold without resort to the concept of the so called affine connections. Buried at advanced points in his presentations is the implied statement that $partial u=du+ast ^{-1}d$ $uast $, the sign at the front of the coderivative term is a matter of whether we include the unit imaginary or not in the definition of Hodge dual, $ast $. We extract and put together the pieces of theory that go into his derivation of that statement, which seems to have gone unnoticed in spite of its relevance for a quick understanding of what his `K\"ahler calculus'. K\"ahler produced a most transparent, compelling and clear formulation of relativistic quantum mechanics (RQM) as a virtual concomitant of his calculus. We shall enumerate several of its notable features, which he failed to emphasize. The exterior calculus in K\"ahler format thus reveals itself as the computational tool for RQM, making the Dirac calculus unnecessary and its difficulties spurious.","PeriodicalId":162928,"journal":{"name":"Fundamental Physics at the Vigier Centenary","volume":"8 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114799416","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

A Clifford Space Generalization of Spacetime: Prospects for Unification in Physics 时空的Clifford空间推广:物理学统一的展望

Fundamental Physics at the Vigier Centenary Pub Date : 2004-11-04 DOI: 10.1142/9789811246463_0011

M. Pavšič

引用次数: 2

Near-Field Analysis of Superluminally Propagating Electromagnetic and Gravitational Fields 超光速传播电磁场和引力场的近场分析

Fundamental Physics at the Vigier Centenary Pub Date : 2003-04-23 DOI: 10.1142/9789811246463_0015

W. Walker

引用次数: 0

Spacetime at the Planck Scale: The Quantum Computer View 普朗克尺度下的时空:量子计算机视角

Fundamental Physics at the Vigier Centenary Pub Date : 2003-04-07 DOI: 10.1142/9789812773258_0030

P. Zizzi

引用次数: 6

Connectivity and the Origin of Inertia 连通性和惯性的起源

Fundamental Physics at the Vigier Centenary Pub Date : 2002-05-30 DOI: 10.1142/9789811246463_0010

L. Nickisch, Jules Mollere

{"title":"Connectivity and the Origin of Inertia","authors":"L. Nickisch, Jules Mollere","doi":"10.1142/9789811246463_0010","DOIUrl":"https://doi.org/10.1142/9789811246463_0010","url":null,"abstract":"Newton's Second Law defines inertial mass as the ratio of the applied force on an object to the responding acceleration of the object (viz., F=ma). Objects that exhibit finite accelerations under finite forces are described as being \"massive'' and this mass has usually been considered to be an innate property of the particles composing the object. However mass itself is never directly measured. It is inertia, the reaction of the object to impressed forces, that is measured. We show that the effects of inertia are equally well explained as a consequence of the vacuum fields acting on massless particles travelling in geodesic motion. In this approach, the vacuum fields in the particle's history define the curvature of the particle's spacetime. The metric describing this curvature implies a transformation to Minkowski spacetime, which we call the Connective transformation. Application of the Connective transformation produces the usual effects of inertia when observed in Minkowski spacetime, including hyperbolic motion in a static electric field (above the vacuum) and uniform motion following an impulse. In the case of the electromagnetic vacuum fields, the motion of the massless charge is a helical motion that can be equated to the particle spin of quantum theory. This spin has the properties expected from quantum theory, being undetermined until \"measured'' by applying a field, and then being found in either a spin up or spin down state. Furthermore, the zitterbewegung of the charge is at the speed of light, again in agreement with quantum theory. Connectivity also allows for pair creation as the Connective transformation can transform positive time intervals in the particle spacetime to negative time intervals in Minkowski spacetime.","PeriodicalId":162928,"journal":{"name":"Fundamental Physics at the Vigier Centenary","volume":"19 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2002-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131833692","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 2