Covariant PhysicsPub Date : 2021-03-02DOI: 10.1093/OSO/9780198864899.003.0001
Moataz H Emam
{"title":"Coordinate Systems and Vectors","authors":"Moataz H Emam","doi":"10.1093/OSO/9780198864899.003.0001","DOIUrl":"https://doi.org/10.1093/OSO/9780198864899.003.0001","url":null,"abstract":"This chapter introduces the various types of coordinate systems that exist in three dimensions and develops the basic concept of ‘metric’ to describe their properties. It introduces vectors in these coordinate systems and develops the notions of the ‘index language,’ dependence on the metric, and the covariance of vectors. Early familiarity with the metric tensor, index or component notation, symmetric and anti-symmetric manipulation is intended.","PeriodicalId":108158,"journal":{"name":"Covariant Physics","volume":"48 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-03-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114551895","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}
Covariant PhysicsPub Date : 1900-01-01DOI: 10.1093/oso/9780198864899.003.0004
Moataz H Emam
{"title":"Special Covariance","authors":"Moataz H Emam","doi":"10.1093/oso/9780198864899.003.0004","DOIUrl":"https://doi.org/10.1093/oso/9780198864899.003.0004","url":null,"abstract":"In this chapter we study the special theory of relativity. We begin with the metric and construct all consequences such as the kinematical quantities, 4-vectors and tensors, Lorentz transformations, geometric interpretations, conservation of 4-momentum and collision problems. We conclude with a discussion of electrodynamics in covariant form.","PeriodicalId":108158,"journal":{"name":"Covariant Physics","volume":"82 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126228052","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}
Covariant PhysicsPub Date : 1900-01-01DOI: 10.1093/oso/9780198864899.003.0009
Moataz H Emam
{"title":"Differential Forms","authors":"Moataz H Emam","doi":"10.1093/oso/9780198864899.003.0009","DOIUrl":"https://doi.org/10.1093/oso/9780198864899.003.0009","url":null,"abstract":"In this chapter we present the modern theory of differential forms and see how it applies to the classical fields studied in the previous chapter. We apply the theory to Maxwell fields as well as to Cartan’s formulation of general relativity. A discussion of the generalized Stokes theorem is given.","PeriodicalId":108158,"journal":{"name":"Covariant Physics","volume":"33 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122320961","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}
Covariant PhysicsPub Date : 1900-01-01DOI: 10.1093/oso/9780198864899.003.0002
Moataz H Emam
{"title":"Tensors","authors":"Moataz H Emam","doi":"10.1093/oso/9780198864899.003.0002","DOIUrl":"https://doi.org/10.1093/oso/9780198864899.003.0002","url":null,"abstract":"In this chapter we develop the concept of tensors, their meaning, and how they arise from vectors. Emphasis is placed on tensor transformations, covariance between coordinate systems, and relation to the metric. The concept of metric connection and the Christoffel symbols is introduced in three dimensions via the easily visualizable idea of parallel transport. Derivatives and intergrals in covariant form are discussed. The first two chapters are designed to familiarize the reader with the language that is the bread and butter of the general theory of relativity and other higher geometric theories.","PeriodicalId":108158,"journal":{"name":"Covariant Physics","volume":"61 24","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114003723","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}
Covariant PhysicsPub Date : 1900-01-01DOI: 10.1093/oso/9780198864899.003.0005
Moataz H Emam
{"title":"General Covariance","authors":"Moataz H Emam","doi":"10.1093/oso/9780198864899.003.0005","DOIUrl":"https://doi.org/10.1093/oso/9780198864899.003.0005","url":null,"abstract":"The general theory of relativity is introduced based on the principle of equivalence. Gravity is shown to arise dues to spacetime curvature. Specific examples of curved spacetimes are presented from the approximate but more intuitive to the complex: Uniform gravitational field (Galilean metric), the Newtonian weak field metric, Schwarzschild’s exterior and interior solutions, black holes, and cosmological spacetimes. A brief discussion on distances, areas and volumes in curved spaces is also given.","PeriodicalId":108158,"journal":{"name":"Covariant Physics","volume":"32 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130214935","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}
Covariant PhysicsPub Date : 1900-01-01DOI: 10.1093/oso/9780198864899.003.0003
Moataz H Emam
{"title":"Classical Covariance","authors":"Moataz H Emam","doi":"10.1093/oso/9780198864899.003.0003","DOIUrl":"https://doi.org/10.1093/oso/9780198864899.003.0003","url":null,"abstract":"Classical mechanics, from point particles through rigid objects and continuum mechanics is reviewed based on the notions of tensors, transformations, and the metric, as developed in the first two chapters. The geodesic equation on flat and curved spaces is introduced and solved in a classical setting. Motion in a potential, particularly a gravitational potential, is discussed. Galilean covariance and transformations are introduced. Time as a fourth dimension is shown to arise even in a classical setting, even if not as rigorous as it would be in relativity theory.","PeriodicalId":108158,"journal":{"name":"Covariant Physics","volume":"6 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126598466","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}
京公网安备 11010802042870号
求助内容：
应助结果提醒方式：