Exploring topics from classical and quantum mechanics and field theory, this book is based on lectures presented in the Graduate Summer School at the Regional Geometry Institute in Park City, Utah, in 1991. The chapter by Bryant treats Lie groups and symplectic geometry, examining not only the connection with mechanics but also the application to differential equations and the recent work of the Gromov school. Rabin's discussion of quantum mechanics and field theory is specifically aimed at mathematicians. Alvarez describes the application of supersymmetry to prove the Atiyah-Singer index theorem, touching on ideas that also underlie more complicated applications of supersymmetry. Quinn's account of the topological quantum field theory captures the formal aspects of the path integral and shows how these ideas can influence branches of mathematics which at first glance may not seem connected. Presenting material at a level between that of textbooks and research papers, much of the book would provide excellent material for graduate courses. The book provides an entree into a field that promises to remain exciting and important for years to come.
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4 of 4 people found the following review helpful:
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Decent survey on "quantum mathematics",
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This review is from: Geometry and Quantum Field Theory: June 22-July 20, 1991, Park City, Utah (Ias/Park City Mathematics, Vol 1) (Paperback)
This book has four articles on mathematics in quantum field theory. Some of it is well known and "classical", particularly the article by Bryant on symplectic geometry (however, Bryan does discuss the modern modern developments by Gromov in the last section). The article by Rabin attempts to do the impossible: try to teach mathematicians the physics behind quantum field theory via path integrals. The article by Alvarez on index theorems summarizes nicely the connections between supersymmetry and index theory. The last article by Quinn on topological field theory is written for the mathematician in mind. It is fascinating mathematics and gives the reader the impression that research in topological field theory will no doubt continue to grow in importance. Several advances have taken place since the book was published (1995), so peruse the literature before buying it.
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Inside This Book
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First Sentence:
From earliest times geometry has been based on physical ideas. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
total homotopy, bordism category, bar involution, homotopy order, incoming boundary, outgoing boundary, clean value, smooth submersion, rational conformal field theories, modularity condition, state modules, tensor category, hermitian structure, symplectic structure, trace algebra, domain category, holomorphic curves, opposite algebra, symplectic reduction, nondegenerate pairings, attaching map, trace ring, bracket algebra, topological quantum field theories, precursor theory Key Phrases - Capitalized Phrases (CAPs): (learn more)
New York, Park City, Chain Rule, Princeton University Press, American Mathematical Society, Calabi Conjecture, Euclidean Green, Regional Geometry Institute, Cambridge University Press, Dan Freed, Differential Geom, Mathematical Methods of Classical Mechanics, Use Proposition New!
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Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
From earliest times geometry has been based on physical ideas. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
total homotopy, bordism category, bar involution, homotopy order, incoming boundary, outgoing boundary, clean value, smooth submersion, rational conformal field theories, modularity condition, state modules, tensor category, hermitian structure, symplectic structure, trace algebra, domain category, holomorphic curves, opposite algebra, symplectic reduction, nondegenerate pairings, attaching map, trace ring, bracket algebra, topological quantum field theories, precursor theory Key Phrases - Capitalized Phrases (CAPs): (learn more)
New York, Park City, Chain Rule, Princeton University Press, American Mathematical Society, Calabi Conjecture, Euclidean Green, Regional Geometry Institute, Cambridge University Press, Dan Freed, Differential Geom, Mathematical Methods of Classical Mechanics, Use Proposition 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 18
books:
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- Partial Differential Relations (Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge A Series of Modern Surveys in Mathematics) by Mikhael Gromov on page 163, and page 179
- Classical Mechanics (3rd Edition) by Herbert Goldstein on page 186, and page 269
- Mathematical Methods of Classical Mechanics (Graduate Texts in Mathematics) by V. I. Arnold on page 179, and page 269
- Field Theory : A Modern Primer (Frontiers in Physics Series, Vol 74) by Pierre Ramond on page 269
- Quantum Mechanics and Path Integrals by Richard P. Feynman on page 269
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