Analytic Hyperbolic Geometry: Mathematical Foundations And Applications
"This new book by Ungar is very well-written, with plenty of references and explanatory pictures. Almost all chapters include exercises which ensure that the book will reach a large audience from undergraduate and graduate students to researchers and academics in different areas of mathematics and mathematical physics. In this book, the author sets out his improved gyrotheory, capturing the curiosity of the reader with discernment, elegance and simplicity." Mathematical Reviews "This book under review provides an efficient algebraic formalism for studying the hyperbolic geometry of Bolyai and Lobachevsky, which underlies Einstein special relativity ... It is of interest both to mathematicians, working in the field of geometry, and the physicists specialized in relativity or quantum computation theory ... It is recommended to graduate students and researchers interested in the interrelations among non-associative algebra, hyperbolic and differential geometry, Einstein relativity theory and the quantum computation theory." Journal of Geometry and Symmetry in Physics "This book represents an exposition of the author's single-handed creation, over the past 17 years, of an algebraic language in which both hyperbolic geometry and special relativity find an aesthetically pleasing formulation, very much like Euclidean geometry and Newtonian mechanics find them in the language of vector spaces." Zentralblatt MATH
Presents a gyrovector space approach to analytic hyperbolic geometry, fully analogous to the well-known vector space approach to Euclidean geometry. Including the definition of gyrogroups, this book presents applications of Mobius gyrovector spaces in quantum computation, and of Einstein gyrovector spaces in special relativity. Les mer
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Presents a gyrovector space approach to analytic hyperbolic geometry, fully analogous to the well-known vector space approach to Euclidean geometry. Including the definition of gyrogroups, this book presents applications of Mobius gyrovector spaces in quantum computation, and of Einstein gyrovector spaces in special relativity.
Detaljer
- Forlag
- World Scientific Publishing Co Pte Ltd
- Innbinding
- Innbundet
- Språk
- Engelsk
- ISBN
- 9789812564573
- Utgivelsesår
- 2005
Anmeldelser
"This new book by Ungar is very well-written, with plenty of references and explanatory pictures. Almost all chapters include exercises which ensure that the book will reach a large audience from undergraduate and graduate students to researchers and academics in different areas of mathematics and mathematical physics. In this book, the author sets out his improved gyrotheory, capturing the curiosity of the reader with discernment, elegance and simplicity." Mathematical Reviews "This book under review provides an efficient algebraic formalism for studying the hyperbolic geometry of Bolyai and Lobachevsky, which underlies Einstein special relativity ... It is of interest both to mathematicians, working in the field of geometry, and the physicists specialized in relativity or quantum computation theory ... It is recommended to graduate students and researchers interested in the interrelations among non-associative algebra, hyperbolic and differential geometry, Einstein relativity theory and the quantum computation theory." Journal of Geometry and Symmetry in Physics "This book represents an exposition of the author's single-handed creation, over the past 17 years, of an algebraic language in which both hyperbolic geometry and special relativity find an aesthetically pleasing formulation, very much like Euclidean geometry and Newtonian mechanics find them in the language of vector spaces." Zentralblatt MATH