**Author**: N.M.J. Woodhouse

**Publisher:** Springer Science & Business Media

**ISBN:**

**Category:** Mathematics

**Page:** 196

**View:** 917

This book provides readers with the tools needed to understand the physical basis of special relativity and will enable a confident mathematical understanding of Minkowski's picture of space-time. It features a large number of examples and exercises, ranging from the rather simple through to the more involved and challenging. Coverage includes acceleration and tensors and has an emphasis on space-time diagrams.

This book presents a powerful way to study Einstein's special theory of relativity and its underlying hyperbolic geometry in which analogies with classical results form the right tool. It introduces the notion of vectors into analytic hyperbolic geometry, where they are called gyrovectors . Newtonian velocity addition is the common vector addition, which is both commutative and associative. The resulting vector spaces, in turn, form the algebraic setting for the standard model of Euclidean geometry. In full analogy, Einsteinian velocity addition is a gyrovector addition, which is both gyrocommutative and gyroassociative . The resulting gyrovector spaces, in turn, form the algebraic setting for the Beltrami-Klein ball model of the hyperbolic geometry of Bolyai and Lobachevsky. Similarly, MAbius addition gives rise to gyrovector spaces that form the algebraic setting for the Poincar(r) ball model of hyperbolic geometry. In full analogy with classical results, the book presents a novel relativistic interpretation of stellar aberration in terms of relativistic gyrotrigonometry and gyrovector addition. Furthermore, the book presents, for the first time, the relativistic center of mass of an isolated system of noninteracting particles that coincided at some initial time t = 0. The novel relativistic resultant mass of the system, concentrated at the relativistic center of mass, dictates the validity of the dark matter and the dark energy that were introduced by cosmologists as ad hoc postulates to explain cosmological observations about missing gravitational force and late-time cosmic accelerated expansion. The discovery of the relativistic center of mass in this book thus demonstrates once again the usefulness of the study of Einstein's special theory of relativity in terms of its underlying analytic hyperbolic geometry. Sample Chapter(s). Chapter 1: Introduction (145 KB). Contents: Gyrogroups; Gyrocommutative Gyrogroups; Gyrogroup Extension; Gyrovectors and Cogyrovectors; Gyrovector Spaces; Rudiments of Differential Geometry; Gyrotrigonometry; Bloch Gyrovector of Quantum Information and Computation; Special Theory of Relativity: The Analytic Hyperbolic Geometric Viewpoint; Relativistic Gyrotrigonometry; Stellar and Particle Aberration. Readership: Undergraduates, graduate students, researchers and academics in geometry, algebra, mathematical physics, theoretical physics and astronomy."

Based on a course taught for years at Oxford, this book offers a concise exposition of the central ideas of general relativity. The focus is on the chain of reasoning that leads to the relativistic theory from the analysis of distance and time measurements in the presence of gravity, rather than on the underlying mathematical structure. Includes links to recent developments, including theoretical work and observational evidence, to encourage further study.

Hermann Minkowski recast special relativity as essentially a new geometric structure for spacetime. This book looks at the ideas of both Einstein and Minkowski, and then introduces the theory of frames, surfaces and intrinsic geometry, developing the main implications of Einstein's general relativity theory.

First published in 1987, this text offers concise but clear explanations and derivations to give readers a confident grasp of the chain of argument that leads from Newton’s laws through Lagrange’s equations and Hamilton’s principle, to Hamilton’s equations and canonical transformations. This new edition has been extensively revised and updated to include: A chapter on symplectic geometry and the geometric interpretation of some of the coordinate calculations. A more systematic treatment of the conections with the phase-plane analysis of ODEs; and an improved treatment of Euler angles. A greater emphasis on the links to special relativity and quantum theory showing how ideas from this classical subject link into contemporary areas of mathematics and theoretical physics. A wealth of examples show the subject in action and a range of exercises – with solutions – are provided to help test understanding.

Einstein's general theory of relativity requires a curved space for the description of the physical world. If one wishes to go beyond superficial discussions of the physical relations involved, one needs to set up precise equations for handling curved space. The well-established mathematical technique that accomplishes this is clearly described in this classic book by Nobel Laureate P.A.M. Dirac. Based on a series of lectures given by Dirac at Florida State University, and intended for the advanced undergraduate, General Theory of Relativity comprises thirty-five compact chapters that take the reader point-by-point through the necessary steps for understanding general relativity.

Intended to follow the usual introductory physics courses, this book has the unique feature of addressing the mathematical needs of sophomores and juniors in physics, engineering and other related fields. Many original, lucid, and relevant examples from the physical sciences, problems at the ends of chapters, and boxes to emphasize important concepts help guide the student through the material. Beginning with reviews of vector algebra and differential and integral calculus, the book continues with infinite series, vector analysis, complex algebra and analysis, ordinary and partial differential equations. Discussions of numerical analysis, nonlinear dynamics and chaos, and the Dirac delta function provide an introduction to modern topics in mathematical physics. This new edition has been made more user-friendly through organization into convenient, shorter chapters. Also, it includes an entirely new section on Probability and plenty of new material on tensors and integral transforms.

للفيزياء الحرارية أهمية كبيرة في فهم العالم الذي نعيش فيه، إذ إن لكل جسم من حولنا هويته الحرارية الخاصة به التي تمنحه خواص فيزيائية مختلفة. إن كتاب (الفيزياء الحرارية) وضع ليوضح علاقة حرارة المواد بما حولها، ويجيب عن كثير من الأسئلة التي يمكن أن تخطر ببالنا. وينقسم كتاب (الفيزياء الحرارية) إلى أربعة أقسام رئيسة، حيث يناقش القسم الأول الأساسيات من مثل القانونين الأول والثاني، والطاقة في الفيزياء الحرارية والتفاعلات والدلالات كالبارامغناطيسية والاتزان الميكانيكي والضغط واتزان وانتشار الجهد الميكانيكي، ويتمحور القسم الثاني حول الثرموديناميكا، والمكائن الحرارية والثلاجات ومكائن الاحتراق الداخلي والماكينة البخارية والطاقة الحرة وتحولاتها. القسم الثالث والأخير من الكتاب يتناول ميكانيكا الإحصاء، كإحصاء بولتزمان والإحصاء الكمّي، وأنظمة الجسيمات المتفاعلة. ويختتم الكتاب بملحقين: الأول عن عناصر ميكانيكا الكمّ والثاني عن النتائج الرياضية. الكتاب يحتوي على تطبيقات في مجالات متعددة، كالكيمياء والجيولوجيا وعلوم الحياة وعلوم البيئة وعلم التعدين وفيزياء الجوامد وفيزياء الفلك، وغيرها مما يساعد على استيعاب أكبر لمفاهيم الفيزياء الحرارية وأسسها. العبيكان للنشر