The aim of this book is to make accessible to mathematicians, physicists, and other scientists interested in quantum theory, the beautiful but mathematically difficult subjects of the Feynman integral and Feynman's operational calculus. There are many advantages to certain approaches to the Feynman integral which are discussed in detail and much of the material covered has only been previously available in research literature. This book not only brings together all the available background material in mathematics and physics that motivates the study of the Feynman integral and Feynman's operational calculus, it also includes detailed proofs for the central results and many new or recently discovered results in one complete volume.
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Editorial Reviews
Review
' A most scholarly text which is comprehensive, detailed and very clearly written. It embraces the whole of the topic not just one part of it, and the historical references give an insight into the development of the ideas behind its fascinating approach to quantum theory.Written by experts who are also good teachers-thoroughly recommended'Islib
' A most scholarly text which is comprehensive, detailed and very clearly written. It embraces the whole of the topic not just one part of it, and the historical references give an insight into the development of the ideas behind its fascinating approach to quantum theory.Written by experts who are also good teachers-thoroughly recommended'Aslib
' A most scholarly te xt which is comprehensive, detailed and very clearly written. It embraces the whole of the topic not just one part of it, and the historical references give an insight into the development of the ideas behind its fascinating approach to quantum theory.Written by experts who are also good teachers-thoroughly recommended'Aslib
' A most scholarly text which is comprehensive, detailed and very clearly written. It embraces the whole of the topic not just one part of it, and the historical references give an insight into the development of the ideas behind its fascinating approach to quantum theory.Written by experts who are also good teachers-thoroughly recommended'Aslib
' A most scholarly te xt which is comprehensive, detailed and very clearly written. It embraces the whole of the topic not just one part of it, and the historical references give an insight into the development of the ideas behind its fascinating approach to quantum theory.Written by experts who are also good teachers-thoroughly recommended'Aslib
About the Author
Gerald W. Johnson, Department of Mathematics and Statistics, University of Nebraska-Lincoln. Michel L. Lapidus, Department of Mathematics, University of California, Riverside.
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Most Helpful Customer Reviews
11 of 12 people found the following review helpful:
5.0 out of 5 stars
An Excellent Volume!,
By Lance Nielsen (Omaha, NE USA) - See all my reviews
This review is from: The Feynman Integral and Feynman's Operational Calculus (Oxford Mathematical Monographs) (Hardcover)
This volume by Johnson and Lapidus is an excellent guide to the Feynman integral and Feynman's operational calculus. The authors bring together a great deal of the background material needed for the study of the integral and operational calculus so as to make the volume mostly self-contained.The book contains several different approaches to the Feynman integral and discusses in some detail relationships between these approaches. The exposition is very clear and detailed and the proofs of results in the text are detailed and extremely well written. Also, the text contains many items that have only appeared in the research literature. Some of these results are quite new. Also contained in this text is a thorough discussion of Feynman's operational calculus, again from more than one point of view. Many of the results contained here have only appeared previously in the research literature and again some are quite recent. This part of the book is also very well and clearly written. There are also many remarks and examples dealing with the applicability of the formalism to physical situations. This is a great read for anyone wanting to further there knowledge about these subjects.
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Inside This Book
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First Sentence:
The main purpose of this book is to provide a mathematical treatment of the Feynman path integral and the related subject of Feyman's operational calculus for noncommuting operators. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
imaginary resolvents, disentangling algebras, singular central potentials, nonperturbative string theory, quantummechanical case, unbounded quadratic forms, strong operator continuous, function space integral, positive continuous additive functionals, singular complex potential, noncommutative operations, distributional differential equation, fractal strings, first representation theorem, combinatorial complications, second representation theorem, deformation quantization, disentangling process, nonzero purely imaginary, product integral representation, heat semigroup, operational calculus, dissipativity condition, strong operator topology, semigroup sense Key Phrases - Capitalized Phrases (CAPs): (learn more)
C-valued Borel, Edward Witten, Mark Kac, Proof Let, Moshe Flato, Richard Feynman, Abelian Chern-Simons, Proof First, Yang Mills, Albert Einstein, Albert Schwarz, Michael Atiyah, Norbert Wiener, Proof Fix, Proof Suppose, Alan Weinstein, Daniel Sternheimer, Jagdish Mehra, Jean Perrin, Proof According, Steven Weinberg New!
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Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
The main purpose of this book is to provide a mathematical treatment of the Feynman path integral and the related subject of Feyman's operational calculus for noncommuting operators. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
imaginary resolvents, disentangling algebras, singular central potentials, nonperturbative string theory, quantummechanical case, unbounded quadratic forms, strong operator continuous, function space integral, positive continuous additive functionals, singular complex potential, noncommutative operations, distributional differential equation, fractal strings, first representation theorem, combinatorial complications, second representation theorem, deformation quantization, disentangling process, nonzero purely imaginary, product integral representation, heat semigroup, operational calculus, dissipativity condition, strong operator topology, semigroup sense Key Phrases - Capitalized Phrases (CAPs): (learn more)
C-valued Borel, Edward Witten, Mark Kac, Proof Let, Moshe Flato, Richard Feynman, Abelian Chern-Simons, Proof First, Yang Mills, Albert Einstein, Albert Schwarz, Michael Atiyah, Norbert Wiener, Proof Fix, Proof Suppose, Alan Weinstein, Daniel Sternheimer, Jagdish Mehra, Jean Perrin, Proof According, Steven Weinberg New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 50
books:
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3
books
cite this book:
- Mathematics and Physics (Progress in Physics - Vol 3) by Jurij (Yu.) Ivanovich Manin on page 696, and Back Matter
- Gauge Fields and Strings (Mathematical Reports,) by Polyakov on page 691, and Back Matter
- Nonlinear Poisson Brackets. Geometry and Quantization (Translations of Mathematical Monographs) by M. V. Karasev and V. P. Maslov in Back Matter
- Quantum Invariants of Knots and 3-Manifolds (De Gruyter Studies in Mathematics) by V. G. Turaev in Back Matter
- Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light by Max Born in Back Matter
See all 50 books this book cites
- The Universality of the Radon Transform (Oxford Mathematical Monographs) by Leon Ehrenpreis in Front Matter
- Quantum Dynamical Systems by Robert Alicki in Back Flap
- Compact Manifolds with Special Holonomy (Oxford Mathematical Monographs) by Dominic D. Joyce in Front Matter
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