The Geometry of Minkowski Spacetime: An Introduction to the Mathematics of the Special Theory of RelativityCourier Corporation, 1 янв. 2003 г. - Всего страниц: 257 This mathematically rigorous treatment examines Zeeman's characterization of the causal automorphisms of Minkowski spacetime and the Penrose theorem concerning the apparent shape of a relativistically moving sphere. Other topics include the construction of a geometric theory of the electromagnetic field; an in-depth introduction to the theory of spinors; and a classification of electromagnetic fields in both tensor and spinor form. Appendixes introduce a topology for Minkowski spacetime and discuss Dirac's famous "Scissors Problem." Appropriate for graduate-level courses, this text presumes only a knowledge of linear algebra and elementary point-set topology. 1992 edition. 43 figures. |
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2-dimensional 3-vectors a(to admissible basis admissible frame admissible observer bilinear form bivector causal automorphism clock components corresponding curve define denote E-continuous E₁ electromagnetic field element equations Euclidean Exercise FAXBY Figure frame of reference future-timelike homeomorphism î¹ implies inner product invariant Lemma light ray Lorentz group Lorentz transformation material particle matrix Minkowski spacetime null cone null vector orthochronous orthonormal basis P-open past null directions past-timelike photon physical Proof R₁ real number relative relativistic rotation satisfies Section Show simultaneous skew-symmetric linear transformation spacelike spacelike vector spatial spin frame spin vector spinor equivalent spinor map spinor of valence ß² subspace suppose symmetric Theorem timelike and future-directed timelike vector topology transformation law v₁ vector space world momentum world tensors world velocity worldline x¹)² Φι
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Стр. 233 - X has an open neighborhood U such that pl(U) is a disjoint union of open sets in X, each of which is mapped homeomorphically onto U by p.
Стр. 150 - The reason for this can be traced to the fact that the...
Стр. 49 - Conversely, if v and w are linearly dependent, then one is a multiple of the other and equality clearly holds in (1.4.1).
Стр. 85 - Lorent2 transformation is completely determined by its effect on any three distinct past null directions. More precisely, given two sets of three distinct past null directions there is one and only one element of...
Стр. 1 - We shall adopt the point of view that the basic problem of science in general is the description of "events" which occur in the physical universe and the analysis of relationships between these events.
Стр. v - It is the intention of this monograph to provide an introduction to the special theory of relativity that is mathematically rigorous and yet spells out in considerable detail the physical significance of the mathematics.
Стр. 227 - Fermions (electrons, protons, neutrons, neutrinos, etc.) possess what the physicists call "half- integer spin" and, as a consequence, their quantum mechanical descriptions ("wave functions") behave in precisely this way...
Стр. 38 - But as the light travels to A, O has moved a short distance to the right of O so that the spherical wavefront observed by O is not concentric with that observed by O.
Стр. 232 - R is connected the proof will be complete if we can show that E is open.
Стр. 48 - M, then (v - w)2 > v2w2 (1.4.1) and equality holds if and only if v and w are linearly dependent. Proof: Consider the vector u — av—bw, where a = v- w and b = v- v = v2.
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Introduction to Geometric Function Theory of Hypercomplex Variables Sorin G. Gal Ограниченный просмотр - 2002 |