The Structures Of Mathematical Physics
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The Structures Of Mathematical Physics
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Author : Steven P. Starkovich
language : en
Publisher: Springer Nature
Release Date : 2021-07-21
The Structures Of Mathematical Physics written by Steven P. Starkovich and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-07-21 with Science categories.
This textbook serves as an introduction to groups, rings, fields, vector and tensor spaces, algebras, topological spaces, differentiable manifolds and Lie groups --- mathematical structures which are foundational to modern theoretical physics. It is aimed primarily at undergraduate students in physics and mathematics with no previous background in these topics. Applications to physics --- such as the metric tensor of special relativity, the symplectic structures associated with Hamilton's equations and the Generalized Stokes's Theorem --- appear at appropriate places in the text. Worked examples, end-of-chapter problems (many with hints and some with answers) and guides to further reading make this an excellent book for self-study. Upon completing this book the reader will be well prepared to delve more deeply into advanced texts and specialized monographs in theoretical physics or mathematics.
The Logical Structure Of Mathematical Physics
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Author : J.D. Sneed
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
The Logical Structure Of Mathematical Physics written by J.D. Sneed 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.
This book is about scientific theories of a particular kind - theories of mathematical physics. Examples of such theories are classical and relativis tic particle mechanics, classical electrodynamics, classical thermodynamics, statistical mechanics, hydrodynamics, and quantum mechanics. Roughly, these are theories in which a certain mathematical structure is employed to make statements about some fragment of the world. Most of the book is simply an elaboration of this rough characterization of theories of mathematical physics. It is argued that each theory of mathematical physics has associated with it a certain characteristic mathematical struc ture. This structure may be used in a variety of ways to make empirical claims about putative applications of the theory. Typically - though not necessarily - the way this structure is used in making such claims requires that certain elements in the structure play essentially different roles. Some playa "theoretical" role; others playa "non-theoretical" role. For example, in classical particle mechanics, mass and force playa theoretical role while position plays a non-theoretical role. Some attention is given to showing how this distinction can be drawn and describing precisely the way in which the theoretical and non-theoretical elements function in the claims of the theory. An attempt is made to say, rather precisely, what a theory of mathematical physics is and how you tell one such theory from anothe- what the identity conditions for these theories are.
The Logical Structure Of Mathematical Physics
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Author : Joseph D. Sneed
language : en
Publisher:
Release Date : 1971
The Logical Structure Of Mathematical Physics written by Joseph D. Sneed and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1971 with Mathematical physics categories.
Quantization Geometry And Noncommutative Structures In Mathematics And Physics
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Author : Alexander Cardona
language : en
Publisher: Springer
Release Date : 2017-10-26
Quantization Geometry And Noncommutative Structures In Mathematics And Physics written by Alexander Cardona and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-10-26 with Science categories.
This monograph presents various ongoing approaches to the vast topic of quantization, which is the process of forming a quantum mechanical system starting from a classical one, and discusses their numerous fruitful interactions with mathematics.The opening chapter introduces the various forms of quantization and their interactions with each other and with mathematics.A first approach to quantization, called deformation quantization, consists of viewing the Planck constant as a small parameter. This approach provides a deformation of the structure of the algebra of classical observables rather than a radical change in the nature of the observables. When symmetries come into play, deformation quantization needs to be merged with group actions, which is presented in chapter 2, by Simone Gutt.The noncommutativity arising from quantization is the main concern of noncommutative geometry. Allowing for the presence of symmetries requires working with principal fiber bundles in a non-commutative setup, where Hopf algebras appear naturally. This is the topic of chapter 3, by Christian Kassel. Nichols algebras, a special type of Hopf algebras, are the subject of chapter 4, by Nicolás Andruskiewitsch. The purely algebraic approaches given in the previous chapters do not take the geometry of space-time into account. For this purpose a special treatment using a more geometric point of view is required. An approach to field quantization on curved space-time, with applications to cosmology, is presented in chapter 5 in an account of the lectures of Abhay Ashtekar that brings a complementary point of view to non-commutativity.An alternative quantization procedure is known under the name of string theory. In chapter 6 its supersymmetric version is presented. Superstrings have drawn the attention of many mathematicians, due to its various fruitful interactions with algebraic geometry, some of which are described here. The remaining chapters discuss further topics, as the Batalin-Vilkovisky formalism and direct products of spectral triples.This volume addresses both physicists and mathematicians and serves as an introduction to ongoing research in very active areas of mathematics and physics at the border line between geometry, topology, algebra and quantum field theory.
Noncommutative Structures In Mathematics And Physics
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Author : Steven Duplij
language : en
Publisher: Springer Science & Business Media
Release Date : 2001-05-31
Noncommutative Structures In Mathematics And Physics written by Steven Duplij 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 2001-05-31 with Science categories.
A presentation of outstanding achievements and ideas, of both eastern and western scientists, both mathematicians and physicists. Their presentations of recent work on quantum field theory, supergravity, M-theory, black holes and quantum gravity, together with research into noncommutative geometry, Hopf algebras, representation theory, categories and quantum groups, take the reader to the forefront of the latest developments. Other topics covered include supergravity and branes, supersymmetric quantum mechanics and superparticles, (super) black holes, superalgebra representations, and SUSY GUT phenomenology. Essential reading for workers in the modern methods of theoretical and mathematical physics.
The Logical Structure Of Mathematical Physics
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Author : Joseph Donald Sneed
language : en
Publisher:
Release Date : 1979
The Logical Structure Of Mathematical Physics written by Joseph Donald Sneed and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1979 with categories.
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.
Introduction To The Mathematical Structure Of Quantum Mechanics An A Short Course For Mathematicians 2nd Edition
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Author : Franco Strocchi
language : en
Publisher: World Scientific Publishing Company
Release Date : 2008-10-30
Introduction To The Mathematical Structure Of Quantum Mechanics An A Short Course For Mathematicians 2nd Edition written by Franco Strocchi and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-10-30 with Science categories.
The second printing contains a critical discussion of Dirac derivation of canonical quantization, which is instead deduced from general geometric structures. This book arises out of the need for Quantum Mechanics (QM) to be part of the common education of mathematics students. The mathematical structure of QM is formulated 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, for a general physical system.The Dirac-von Neumann axioms are then derived. The description of states and observables as Hilbert space vectors and operators follows from the GNS and Gelfand-Naimark Theorems. The experimental existence of complementary observables for atomic systems is shown to imply the noncommutativity of the observable algebra, the distinctive feature of QM; for finite degrees of freedom, the Weyl algebra codifies the experimental complementarity of position and momentum (Heisenberg commutation relations) and Schrödinger QM follows from the von Neumann uniqueness theorem.The existence problem of the dynamics is related to the self-adjointness of the Hamiltonian and solved by the Kato-Rellich conditions on the potential, which also guarantee quantum stability for classically unbounded-below Hamiltonians. Examples are discussed which include the explanation of the discreteness of the atomic spectra.Because of the increasing interest in the relation between QM and stochastic processes, a final chapter is devoted to the functional integral approach (Feynman-Kac formula), to the formulation in terms of ground state correlations (the quantum mechanical analog of the Wightman functions) and their analytic continuation to imaginary time (Euclidean QM). The quantum particle on a circle is discussed in detail, as an example of the interplay between topology and functional integral, leading to the emergence of superselection rules and θ sectors.
The Structure And Interpretation Of The Standard Model
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Author : Gordon McCabe
language : en
Publisher: Elsevier
Release Date : 2011-08-30
The Structure And Interpretation Of The Standard Model written by Gordon McCabe and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-08-30 with Science categories.
This book provides a philosophically informed and mathematically rigorous introduction to the 'standard model' of particle physics. The standard model is the currently accepted and experimentally verified model of all the particles and interactions in our universe. All the elementary particles in our universe, and all the non-gravitational interactions -the strong nuclear force, the weak nuclear force, and the electromagnetic force - are collected together and, in the case of the weak and electromagnetic forces, unified in the standard model. Rather than presenting the calculational recipes favored in most treatments of the standard model, this text focuses upon the elegant mathematical structures and the foundational concepts of the standard model.· Combines an exposition of the philosophical foundations and rigorous mathematical structure of particle physics· Demonstrates the standard model with elegant mathematics, rather than a medley of computational recipes· Promotes a group-theoretical and fibre-bundle approach to the standard model, rather than the Lagrangian approach favoured by calculationalists· Explains the different approaches to particle physics and the standard model which can be found within the literature
The Structure And Dynamics Of Theories
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Author : Wolfgang Stegmüller
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-11
The Structure And Dynamics Of Theories written by Wolfgang Stegmüller 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 2013-11-11 with Business & Economics categories.
The first part of this book, Part I, can be read from two quite distinct points of view: one, as an attempt to develop and defend the important aspects of an entirely new approach to the analysis of the structure of scientific the ories; and second, as the source of the conceptual apparatus needed for the analysis of theory dynamics and the metascientific reconstruction of T. S. Kuhn's notions of 'normal science' and 'scientific revolutions. ' In the last few years a great deal has been written about Kuhnian 'irra tionalism' and 'relativism. ' Most writers felt that they must combat it; a few thought that they must develop it further and deploy it propagandistically against a 'logic of science. ' According to the view developed in Part II of this book, both parties are on the wrong track. As far as irrationalism is concerned, it must be said that Kuhn's position itself cannot be characterized as 'irrational' in any reasonable sense of the word. His language is much too clear, and his examples are historically too well founded. (He is thoroughly aware of his frequent use of metaphorical language which, as can also be shown, is his prerogative. ) Without precedent in his work is the fact that he appears to impute irrational behavior to the practioners of the exact natural sciences (of all people!).