The Story of Quantum Mechanics

"Clear and coherent … One of the most exciting aspects of the book is the author's account of how the consequences and implications of the breakthroughs in quantum mechanics challenged the mechanistic, deterministic philosophy fostered by classical science." — The Science Teacher Written by a respected Harvard physicist who did his doctoral work in Munich among many of the founding fathers of quantum mechanics, this introductory account of the evolution of quantum physics also explores the subject's philosophical implications. Beginning with brief background sketches, the author offers an absorbing narrative of the discovery of the principles of quantum mechanics as well as an assessment of their validity and significance. The opening chapters trace the development of physics from antiquity onward, chronicling the origins of quantum mechanics and the ways in which quantum theory was used to address previously unsolved problems and to interpret observable atomic phenomena. Succeeding chapters are devoted to matters at the forefront of research pertaining to elementary particles, and the text concludes with a look at the old and new concepts of physical science and their relationship to issues of philosophy and religion — including considerations of causality, determinism, and free will. Includes 36 black-and-white figures, 12 halftones, five tables, and a Glossary of Scientific Terms.

Politics & Social Sciences

Guillemin, Victor

Philosophy

Dover Publications

"Clear and coherent … One of the most exciting aspects of the book is the author's account of how the consequences and implications of the breakthroughs in quantum mechanics challenged the mechanistic, deterministic philosophy fostered by classical science." — The Science TeacherWritten by a respected Harvard physicist who did his doctoral work in Munich among many of the founding fathers of quantum mechanics, this introductory account of the evolution of quantum physics also explores the subject's philosophical implications. Beginning with brief background sketches, the author offers an absorbing narrative of the discovery of the principles of quantum mechanics as well as an assessment of their validity and significance.The opening chapters trace the development of physics from antiquity onward, chronicling the origins of quantum mechanics and the ways in which quantum theory was used to address previously unsolved problems and to interpret observable atomic phenomena. Succeeding chapters are devoted to matters at the forefront of research pertaining to elementary particles, and the text concludes with a look at the old and new concepts of physical science and their relationship to issues of philosophy and religion — including considerations of causality, determinism, and free will. Includes 36 black-and-white figures, 12 halftones, five tables, and a Glossary of Scientific Terms.

Symplectic Fibrations and Multiplicity Diagrams

Multiplicity diagrams can be viewed as schemes for describing the phenomenon of "symmetry breaking" in quantum physics. The subject of this book is the multiplicity diagrams associated with the classical groups U(n), O(n), etc. It presents such topics as asymptotic distributions of multiplicities, hierarchical patterns in multiplicity diagrams, lacunae, and the multiplicity diagrams of the rank 2 and rank 3 groups. The authors take a novel approach, using the techniques of symplectic geometry. The book develops in detail some themes which were touched on in the highly successful Symplectic Techniques in Physics by V. Guillemin and S. Sternberg (CUP, 1984) , including the geometry of the moment map, the Duistermaat-Heckman theorem, the interplay between coadjoint orbits and representation theory, and quantization. Students and researchers in geometry and mathematical physics will find this book fascinating.

Science & Math

Sternberg, Shlomo

Lerman, Eugene

Mathematics

Cambridge University Press

Symplectic geometry is very useful for formulating clearly and concisely problems in classical physics and also for understanding the link between classical problems and their quantum counterparts. It is thus a subject of interest to both mathematicians and physicists, though they have approached the subject from different viewpoints. This is the first book that attempts to reconcile these approaches. The authors use the uncluttered, coordinate-free approach to symplectic geometry and classical mechanics that has been developed by mathematicians over the course of the past thirty years, but at the same time apply the apparatus to a great number of concrete problems. Some of the themes emphasized in the book include the pivotal role of completely integrable systems, the importance of symmetries, analogies between classical dynamics and optics, the importance of symplectic tools in classical variational theory, symplectic features of classical field theories, and the principle of general covariance.

Symplectic Techniques in Physics

Based on a seminar sponsored by the Institute for Advanced Study in 1977-1978, this set of papers introduces micro-local analysis concisely and clearly to mathematicians with an analytical background. The papers treat the theory of microfunctions and applications such as boundary values of elliptic partial differential equations, propagation of singularities in the vicinity of degenerate characteristics, holonomic systems, Feynman integrals from the hyperfunction point of view, and harmonic analysis on Lie groups.

Seminar on Micro-Local Analysis. (AM-93), Volume 93 (Annals of Mathematics Studies, 93)

Kashiwara, Masaki

Kawai, Takahiro

Princeton University Press

Based on a seminar sponsored by the Institute for Advanced Study in 1977-1978, this set of papers introduces micro-local analysis concisely and clearly to mathematicians with an analytical background. The papers treat the theory of microfunctions and applications such as boundary values of elliptic partial differential equations, propagation of singularities in the vicinity of degenerate characteristics, holonomic systems, Feynman integrals from the hyperfunction point of view, and harmonic analysis on Lie groups.

The theory of Toeplitz operators has come to resemble more and more in recent years the classical theory of pseudodifferential operators. For instance, Toeplitz operators possess a symbolic calculus analogous to the usual symbolic calculus, and by symbolic means one can construct parametrices for Toeplitz operators and create new Toeplitz operators out of old ones by functional operations.
 If P is a self-adjoint pseudodifferential operator on a compact manifold with an elliptic symbol that is of order greater than zero, then it has a discrete spectrum. Also, it is well known that the asymptotic behavior of its eigenvalues is closely related to the behavior of the bicharacteristic flow generated by its symbol.
 It is natural to ask if similar results are true for Toeplitz operators. In the course of answering this question, the authors explore in depth the analogies between Toeplitz operators and pseudodifferential operators and show that both can be viewed as the "quantized" objects associated with functions on compact contact manifolds.

The Spectral Theory of Toeplitz Operators (Annals of Mathematics Studies)

Boutet de Monvel, L.

The subject matter of this work is an area of Lorentzian geometry which has not been heretofore much investigated: Do there exist Lorentzian manifolds all of whose light-like geodesics are periodic? A surprising fact is that such manifolds exist in abundance in (2 + 1)-dimensions (though in higher dimensions they are quite rare). This book is concerned with the deformation theory of M2,1 (which furnishes almost all the known examples of these objects). It also has a section describing conformal invariants of these objects, the most interesting being the determinant of a two dimensional "Floquet operator," invented by Paneitz and Segal.

Cosmology in (2 + 1) -Dimensions, Cyclic Models, and Deformations of M2,1. (AM-121), Volume 121 (Annals of Mathematics Studies, 121)

Astronomy & Space Science

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Books by Guillemin, Victor

See the best price to sell, buy, or rent books by Guillemin, Victor. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

The Story of Quantum Mechanics

The Story of Quantum Mechanics

Symplectic Fibrations and Multiplicity Diagrams

Symplectic Techniques in Physics

Symplectic Techniques in Physics

Symplectic Fibrations and Multiplicity Diagrams

Seminar on Micro-Local Analysis. (AM-93), Volume 93 (Annals of Mathematics Studies, 93)

Seminar on Micro-Local Analysis. (AM-93), Volume 93 (Annals of Mathematics Studies, 93)

The Spectral Theory of Toeplitz Operators (Annals of Mathematics Studies)

Cosmology in (2 + 1) -Dimensions, Cyclic Models, and Deformations of M2,1. (AM-121), Volume 121 (Annals of Mathematics Studies, 121)