The Mathematical Structure Of Classical And Relativistic Physics
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The Mathematical Structure Of Classical And Relativistic Physics
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Author : Enzo Tonti
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-09-07
The Mathematical Structure Of Classical And Relativistic Physics written by Enzo Tonti and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-09-07 with Science categories.
The theories describing seemingly unrelated areas of physics have surprising analogies that have aroused the curiosity of scientists and motivated efforts to identify reasons for their existence. Comparative study of physical theories has revealed the presence of a common topological and geometric structure. The Mathematical Structure of Classical and Relativistic Physics is the first book to analyze this structure in depth, thereby exposing the relationship between (a) global physical variables and (b) space and time elements such as points, lines, surfaces, instants, and intervals. Combining this relationship with the inner and outer orientation of space and time allows one to construct a classification diagram for variables, equations, and other theoretical characteristics. The book is divided into three parts. The first introduces the framework for the above-mentioned classification, methodically developing a geometric and topological formulation applicable to all physical laws and properties; the second applies this formulation to a detailed study of particle dynamics, electromagnetism, deformable solids, fluid dynamics, heat conduction, and gravitation. The third part further analyses the general structure of the classification diagram for variables and equations of physical theories. Suitable for a diverse audience of physicists, engineers, and mathematicians, The Mathematical Structure of Classical and Relativistic Physics offers a valuable resource for studying the physical world. Written at a level accessible to graduate and advanced undergraduate students in mathematical physics, the book can be used as a research monograph across various areas of physics, engineering and mathematics, and as a supplemental text for a broad range of upper-level scientific coursework.
Mathematical Physics Classical Mechanics
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Author : Andreas Knauf
language : en
Publisher: Springer
Release Date : 2018-02-24
Mathematical Physics Classical Mechanics written by Andreas Knauf and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-02-24 with Science categories.
As a limit theory of quantum mechanics, classical dynamics comprises a large variety of phenomena, from computable (integrable) to chaotic (mixing) behavior. This book presents the KAM (Kolmogorov-Arnold-Moser) theory and asymptotic completeness in classical scattering. Including a wealth of fascinating examples in physics, it offers not only an excellent selection of basic topics, but also an introduction to a number of current areas of research in the field of classical mechanics. Thanks to the didactic structure and concise appendices, the presentation is self-contained and requires only knowledge of the basic courses in mathematics. The book addresses the needs of graduate and senior undergraduate students in mathematics and physics, and of researchers interested in approaching classical mechanics from a modern point of view.
Physics For Mathematicians
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Author : Michael Spivak
language : en
Publisher:
Release Date : 2010
Physics For Mathematicians written by Michael Spivak and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Mechanics categories.
Relativity On Curved Manifolds
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Author : F. de Felice
language : en
Publisher: Cambridge University Press
Release Date : 1990
Relativity On Curved Manifolds written by F. de Felice and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990 with Mathematics categories.
General relativity is now essential to the understanding of modern physics, but the power of the theory cannot be exploited fully without a detailed knowledge of its mathematical structure. This book aims to implement this structure, and then to develop those applications that have been central to the growth of the theory.
The Special Theory Of Relativity
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Author : Anadijiban Das
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
The Special Theory Of Relativity written by Anadijiban Das and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Science categories.
Based on courses taught at the University of Dublin, Carnegie Mellon University, and mostly at Simon Fraser University, this book presents the special theory of relativity from a mathematical point of view. It begins with the axioms of the Minkowski vector space and the flat spacetime manifold. Then it discusses the kinematics of special relativity in terms of Lorentz tranformations, and treats the group structure of Lorentz transformations. Extending the discussion to spinors, the author shows how a unimodular mapping of spinor (vector) space can induce a proper, orthochronous Lorentz mapping on the Minkowski vector space. The second part begins with a discussion of relativistic particle mechanics from both the Lagrangian and Hamiltonian points of view. The book then turns to the relativistic (classical) field theory, including a proof of Noether's theorem and discussions of the Klein-Gordon, electromagnetic, Dirac, and non-abelian gauge fields. The final chapter deals with recent work on classical fields in an eight-dimensional covariant phase space.
Relativistic Quantum Mechanics
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Author : Hartmut Pilkuhn
language : en
Publisher: Springer Science & Business Media
Release Date : 2005-08-03
Relativistic Quantum Mechanics written by Hartmut Pilkuhn and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-08-03 with Science categories.
In this book, quantum mechanics is developed from the outset on a relativistic basis, using the superposition principle, Lorentz invariance and gauge invariance. Nonrelativistic quantum mechanics as well as classical relativistic mechanics appear as special cases. They are the sources of familiar names such as "orbital angular momentum", "spin-orbit coupling" and "magnetic moment" for operators of the relativistic quantum formalism. The theory of binaries, in terms of differential equations, is treated for the first time in this book. These have the mathematical structure of the corresponding one-body equations (Klein-Gordon for two spinless particles, Dirac for two spinor particles) with a relativistically reduced mass. They allow the calculation of radiative corrections via the vector potential operator. This second edition of the successful textbook adds various new sections on relativistic quantum chemistry and on the relativistic treatment of the proton in hydrogen. Others chapters have been expanded, e.g. on hyperfinite interactions, or carefully revisited.
An Introduction To The Mathematical Structure Of Quantum Mechanics
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Author : F. Strocchi
language : en
Publisher: World Scientific
Release Date : 2008
An Introduction To The Mathematical Structure Of Quantum Mechanics written by F. Strocchi and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Science categories.
Arising out of the need for Quantum Mechanics (QM) to be part of the common education of mathematics students, this book formulates the mathematical structure of QM in terms of the C*-algebra of observables, which is argued on the basis of the operational definition of measurements and the duality between states and observables.
The Mathematical Structure Of Stable Physical Systems
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Author : Dr. Martin Concoyle & G.P. Coatmundi
language : en
Publisher: Trafford Publishing
Release Date : 2014
The Mathematical Structure Of Stable Physical Systems written by Dr. Martin Concoyle & G.P. Coatmundi and has been published by Trafford Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014 with Education categories.
This book is an introduction to the simple math patterns used to describe fundamental, stable spectral-orbital physical systems (represented as discrete hyperbolic shapes), the containment set has many-dimensions, and these dimensions possess macroscopic geometric properties (which are also discrete hyperbolic shapes). Thus, it is a description which transcends the idea of materialism (ie it is higher-dimensional), and it can also be used to model a life-form as a unified, high-dimension, geometric construct, which generates its own energy, and which has a natural structure for memory, where this construct is made in relation to the main property of the description being, in fact, the spectral properties of both material systems and of the metric-spaces which contain the material systems, where material is simply a lower dimension metric-space, and where both material-components and metric-spaces are in resonance with the containing space. Partial differential equations are defined on the many metric-spaces of this description, but their main function is to act on either the, usually, unimportant free-material components (to most often cause non-linear dynamics) or to perturb the orbits of the, quite often condensed, material trapped by (or within) the stable orbits of a very stable hyperbolic metric-space shape.
Introduction To Relativistic Statistical Mechanics
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Author : Rmi Hakim
language : en
Publisher: World Scientific
Release Date : 2011
Introduction To Relativistic Statistical Mechanics written by Rmi Hakim and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with Science categories.
This is one of the very few books focusing on relativistic statistical mechanics, and is written by a leading expert in this special field. It started from the notion of relativistic kinetic theory, half a century ago, exploding into relativistic statistical mechanics. This will interest specialists of various fields, especially the (classical and quantum) plasma physics. However, quantum physics ? to which a major part is devoted ? will be of more interest since, not only it applies to quantum plasma physics, but also to nuclear matter and to strong magnetic field, cosmology, etc. Although the domain of gauge theory is not covered in this book, the topic is not completely forgotten, in particular in the domain of plasma physics. This book is particularly readable for graduate students and a fortiori to young researchers for whom it offers methods and also appropriate schemes to deal with the current problems encountered in astrophysics, in strong magnetic, in nuclear or even in high energy physics.
Geometric Formulation Of Classical And Quantum Mechanics
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Author : G. Giachetta
language : en
Publisher: World Scientific
Release Date : 2011
Geometric Formulation Of Classical And Quantum Mechanics written by G. Giachetta and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with Science categories.
The geometric formulation of autonomous Hamiltonian mechanics in the terms of symplectic and Poisson manifolds is generally accepted. This book provides the geometric formulation of non-autonomous mechanics in a general setting of time-dependent coordinate and reference frame transformations.