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Springer series in operations research/Springer series in operations research and financial engineering

Introduction to Foundations

A. B. Dieker, Steven T. Hackman

Published Sep 24, 2024• 1 citation
Publisher

Abstract

Abstract In Part III, we provide the mathematical foundations of the QPLEX methodology. While the material presented in this part is self-contained from a mathematical perspective, it heavily uses the results presented in Chaps. 11 and 12 .
DOI
10.1007/978-3-031-74870-7_15

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This 2004 textbook provides a pedagogical introduction to the formalism, foundations and applications of quantum mechanics. Part I covers the basic material which is necessary to understand the transition from classical to wave mechanics. Topics include classical dynamics, with emphasis on canonical transformations and the Hamilton-Jacobi equation, the Cauchy problem for the wave equation, Helmholtz equation and eikonal approximation, introduction to spin, perturbation theory and scattering theory. The Weyl quantization is presented in Part II, along with the postulates of quantum mechanics. Part III is devoted to topics such as statistical mechanics and black-body radiation, Lagrangian and phase-space formulations of quantum mechanics, and the Dirac equation. This book is intended for use as a textbook for beginning graduate and advanced undergraduate courses. It is self-contained and includes problems to aid the reader's understanding.
Abstract The aim of this volume of essays is to delineate and examine a range of topics which represent a systematic account of the nature and implications of QFT. The contributors, who include Michael Redhead, James T. Cushing, Paul Teller, and Gordon Fleming, approach QFT from a variety of standpoints. Part I offers two different interpretations of the value of studying the foundations of QFT as an area of separate metaphysical research. Parts II and III consider the metaphysical and methodological implications of such issues as the problem of the status of virtual particles; the technique of renormalization; and the role of covariance principles. Part IV examines the mathematical foundations of QFT.
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