Gauge Integral Structures For Stochastic Calculus And Quantum Electrodynamics

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Gauge Integral Structures For Stochastic Calculus And Quantum Electrodynamics
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Author : Patrick Muldowney
language : en
Publisher: John Wiley & Sons
Release Date : 2021-04-23
Gauge Integral Structures For Stochastic Calculus And Quantum Electrodynamics written by Patrick Muldowney and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-04-23 with Mathematics categories.
GAUGE INTEGRAL STRUCTURES FOR STOCHASTIC CALCULUS AND QUANTUM ELECTRODYNAMICS A stand-alone introduction to specific integration problems in the probabilistic theory of stochastic calculus Picking up where his previous book, A Modern Theory of Random Variation, left off, Gauge Integral Structures for Stochastic Calculus and Quantum Electrodynamics introduces readers to particular problems of integration in the probability-like theory of quantum mechanics. Written as a motivational explanation of the key points of the underlying mathematical theory, and including ample illustrations of the calculus, this book relies heavily on the mathematical theory set out in the author’s previous work. That said, this work stands alone and does not require a reading of A Modern Theory of Random Variation in order to be understandable. Gauge Integral Structures for Stochastic Calculus and Quantum Electrodynamics takes a gradual, relaxed, and discursive approach to the subject in a successful attempt to engage the reader by exploring a narrower range of themes and problems. Organized around examples with accompanying introductions and explanations, the book covers topics such as: Stochastic calculus, including discussions of random variation, integration and probability, and stochastic processes Field theory, including discussions of gauges for product spaces and quantum electrodynamics Robust and thorough appendices, examples, illustrations, and introductions for each of the concepts discussed within An introduction to basic gauge integral theory (for those unfamiliar with the author’s previous book) The methods employed in this book show, for instance, that it is no longer necessary to resort to unreliable “Black Box” theory in financial calculus; that full mathematical rigor can now be combined with clarity and simplicity. Perfect for students and academics with even a passing interest in the application of the gauge integral technique pioneered by R. Henstock and J. Kurzweil, Gauge Integral Structures for Stochastic Calculus and Quantum Electrodynamics is an illuminating and insightful exploration of the complex mathematical topics contained within.
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Author :
language : en
Publisher: John Wiley & Sons
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written by and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.
U S Government Research Development Reports
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Author :
language : en
Publisher:
Release Date : 1969-10
U S Government Research Development Reports written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1969-10 with Science categories.
Nuclear Science Abstracts
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Author :
language : en
Publisher:
Release Date : 1976
Nuclear Science Abstracts written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1976 with Nuclear energy categories.
Energy Research Abstracts
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Author :
language : en
Publisher:
Release Date : 1988
Energy Research Abstracts written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988 with Power resources categories.
Stochastic Processes Physics And Geometry Ii Proceedings Of The Iii International Conference
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Author : Sergio Albeverio
language : en
Publisher: World Scientific
Release Date : 1995-02-17
Stochastic Processes Physics And Geometry Ii Proceedings Of The Iii International Conference written by Sergio Albeverio and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-02-17 with categories.
As was already evident from the previous two meetings, the theory of stochastic processes, the study of geometrical structures, and the investigation of certain physical problems are inter-related. In fact the trend in recent years has been towards stronger interactions between these areas. As a result, a large component of the contributions is concerned with the theory of stochastic processes, quantum theory, and their relations.
Physics Briefs
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Author :
language : en
Publisher:
Release Date : 1993
Physics Briefs written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993 with Physics categories.
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.
Scientific And Technical Aerospace Reports
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Author :
language : en
Publisher:
Release Date : 1994
Scientific And Technical Aerospace Reports written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with Aeronautics categories.
Quantum Field Theory I Basics In Mathematics And Physics
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Author : Eberhard Zeidler
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-04-18
Quantum Field Theory I Basics In Mathematics And Physics written by Eberhard Zeidler 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 2007-04-18 with Science categories.
This is the first volume of a modern introduction to quantum field theory which addresses both mathematicians and physicists, at levels ranging from advanced undergraduate students to professional scientists. The book bridges the acknowledged gap between the different languages used by mathematicians and physicists. For students of mathematics the author shows that detailed knowledge of the physical background helps to motivate the mathematical subjects and to discover interesting interrelationships between quite different mathematical topics. For students of physics, fairly advanced mathematics is presented, which goes beyond the usual curriculum in physics.