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MATHEMATICAL PHYSICS
ANALYTIC HYPERBOLIC GEOMETRY AND ALBERT EINSTEIN’S SPECIAL THEORY OF RELATIVITY (2nd Edition)
by Abraham Albert Ungar (North Dakota State University, USA) 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. The premise of analogy as a study strategy is to make the unfamiliar familiar. Accordingly, this book introduces the notion of vectors into analytic hyperbolic geometry, where they are called gyrovectors. Gyrovectors turn out to be equivalence classes that add according to the gyroparallelogram law just as vectors are equivalence classes that add according to the parallelogram law. In the gyrolanguage of this book, accordingly, one prefixes a gyro to a classical term to mean the analogous term in hyperbolic geometry. As an example, the relativistic gyrotrigonometry of Einstein’s special relativity is developed and employed to the study of the stellar aberration phenomenon in astronomy. 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; Enriched Special Relativity Theory: Special Relativity of Signature (m, n). Readership: The book is aimed at a large audience. It includes both elementary and advanced topics, and is structured so it can be enjoyed equally by undergraduates, graduate students, researchers and academics.
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730pp Feb 2022 978-981-124-410-0 US$198 £175 LECTURES ON QUANTUM MECHANICS AND ATTRACTORS
by Alexander Komech (Russian Academy of Sciences, Russia & Lomonosov Moscow State University, Russia & Vienna University, Austria) This book gives a concise introduction to Quantum Mechanics with a systematic, coherent, and in-depth explanation of related mathematical methods from the scattering theory and the theory of Partial Differential Equations. The book utilizes elementary mathematical derivations. The presentation assumes only basic knowledge of the origin of Hamiltonian mechanics, Maxwell equations, calculus, Ordinary Differential Equations and basic PDEs. Key topics include the Schrö dinger, Pauli, and Dirac equations, the corresponding conservation laws, spin, the hydrogen spectrum, and the Zeeman effect, scattering of light and particles, photoelectric effect, electron diffraction, and relations of quantum postulates with attractors of nonlinear Hamiltonian PDEs. Featuring problem sets and accompanied by extensive contemporary and historical references, this book could be used for the course on Quantum Mechanics and is also suitable for individual study. Contents: Nonrelativistic Quantum Mechanics; Scattering of Light and Particles; Atom in Magnetic Field; Relativistic Quantum Mechanics; Quantum Postulates and Attractors; Attractors of Hamiltonian PDEs; Old Quantum Theory; Noether Theory of Invariants; Stationary Perturbation Theory. Readership: Graduate students and advanced undergraduate students physicists, chemists and mathematicians, lecturers in Quantum Mechanics.
