John C. Baez's Books

Gauge Fields, Knots And Gravity

By: John C Baez,Javier P Muniain

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Gauge Fields, Knots And Gravity

By: John C Baez,Javier P Muniain

This is an introduction to the basic tools of mathematics needed to understand the relation between knot theory and quantum gravity. The book begins with a rapid course on manifolds and differential forms, emphasizing how these provide a proper language for formulating Maxwell's equations on arbitrary spacetimes. The authors then introduce vector bundles, connections and curvature in order to generalize Maxwell theory to the Yang-Mills equations. The relation of gauge theory to the newly discovered knot invariants such as the Jones polynomial is sketched. Riemannian geometry is then introduced in order to describe Einstein's equations of general relativity and show how an attempt to quantize gravity leads to interesting applications of knot theory.

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Page Count

481

Publisher

World Scientific Publishing Company

Published Date

ISBN 10

9813103248

ISBN 13

9789813103245

Introduction to Algebraic and Constructive Quantum Field Theory

By: John C. Baez,Irving E. Segal,Zhengfang Zhou

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Introduction to Algebraic and Constructive Quantum Field Theory

By: John C. Baez,Irving E. Segal,Zhengfang Zhou

The authors present a rigorous treatment of the first principles of the algebraic and analytic core of quantum field theory. Their aim is to correlate modern mathematical theory with the explanation of the observed process of particle production and of particle-wave duality that heuristic quantum field theory provides. Many topics are treated here in book form for the first time, from the origins of complex structures to the quantization of tachyons and domains of dependence for quantized wave equations. This work begins with a comprehensive analysis, in a universal format, of the structure and characterization of free fields, which is illustrated by applications to specific fields. Nonlinear local functions of both free fields (or Wick products) and interacting fields are established mathematically in a way that is consistent with the basic physical constraints and practice. Among other topics discussed are functional integration, Fourier transforms in Hilbert space, and implementability of canonical transformations. The authors address readers interested in fundamental mathematical physics and who have at least the training of an entering graduate student. A series of lexicons connects the mathematical development with the underlying physical motivation or interpretation. The examples and problems illustrate the theory and relate it to the scientific literature. Originally published in 1992. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

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Page Count

310

Publisher

Princeton University Press

Published Date

ISBN 10

1400862507

ISBN 13

9781400862504

Quantum Techniques In Stochastic Mechanics

By: John C Baez,Jacob D Biamonte

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Quantum Techniques In Stochastic Mechanics

By: John C Baez,Jacob D Biamonte

We introduce the theory of chemical reaction networks and their relation to stochastic Petri nets — important ways of modeling population biology and many other fields. We explain how techniques from quantum mechanics can be used to study these models. This relies on a profound and still mysterious analogy between quantum theory and probability theory, which we explore in detail. We also give a tour of key results concerning chemical reaction networks and Petri nets.

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Page Count

276

Publisher

World Scientific

Published Date

ISBN 10

981322696X

ISBN 13

9789813226968

Infinite-Dimensional Representations of 2-Groups

By: John C. Baez

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Infinite-Dimensional Representations of 2-Groups

By: John C. Baez

Just as groups can have representations on vector spaces, 2-groups have representations on 2-vector spaces, but Lie 2-groups typically have few representations on the finite-dimensional 2-vector spaces introduced by Kapranov and Voevodsky. Therefore, Crane, Sheppeard, and Yetter introduced certain infinite-dimensional 2-vector spaces, called measurable categories, to study infinite-dimensional representations of certain Lie 2-groups, and German and North American mathematicians continue that work here. After introductory matters, they cover representations of 2-groups, and measurable categories, representations on measurable categories. There is no index. Annotation ©2012 Book News, Inc., Portland, OR (booknews.com).

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Page Count

133

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821872842

ISBN 13

9780821872840

Goldmine Records & Prices

By: John Koenig

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Goldmine Records & Prices

By: John Koenig

In addition to listings for more than 30,000 American records of the 1950s-1980s, this edition also provides current collector pricing for every record listing, giving collectors more information for their dollar.

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Page Count

628

Publisher

Krause Publications

Published Date

ISBN 10

0896893871

ISBN 13

9780896893870

Book's by John C. Baez

Gauge Fields, Knots And Gravity

Gauge Fields, Knots And Gravity

Introduction to Algebraic and Constructive Quantum Field Theory

Introduction to Algebraic and Constructive Quantum Field Theory

Quantum Techniques In Stochastic Mechanics

Quantum Techniques In Stochastic Mechanics

Infinite-Dimensional Representations of 2-Groups

Infinite-Dimensional Representations of 2-Groups

Goldmine Records & Prices

Goldmine Records & Prices

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