Constitutions of Matter: Mathematically Modeling the Most Everyday of Physical Phenomena

Constitutions of Matter: Mathematically Modeling the Most Everyday of Physical Phenomena

by Martin H. Krieger
     
 

ISBN-10: 0226453057

ISBN-13: 9780226453057

Pub. Date: 04/28/1998

Publisher: University of Chicago Press

In this insightful work, Martin H. Krieger shows what physicists are really doing behind the nearly impenetrable cloud of mathematical models they use as research tools. He argues that the technical details of these complex calculations serve not only as a means to an end, but also reveal key aspects of the physical properties they model. Using two tours de force of…  See more details below

Overview

In this insightful work, Martin H. Krieger shows what physicists are really doing behind the nearly impenetrable cloud of mathematical models they use as research tools. He argues that the technical details of these complex calculations serve not only as a means to an end, but also reveal key aspects of the physical properties they model. Using two tours de force of modern physics as case studies - proofs that ordinary matter is stable, and solutions to the Ising model of a phase transition (how a liquid freezes to a solid, for instance) - Krieger uncovers the philosophical foundations on which the mathematical models of these phenomena are built. In so doing, he gives the reader a better feel not just for how physicists believe the natural world is structured, but also for how they have arrived at those conclusions. Krieger's lucid discussions will help students of physics and applied mathematics appreciate the larger physical issues behind the mathematical details of modern physics. Historians and philosophers of science will gain deeper insights into how theoretical physicists do science, while technically advanced general readers will get a rare, behind-the-scenes glimpse into the world of modern physics.

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Product Details

ISBN-13:
9780226453057
Publisher:
University of Chicago Press
Publication date:
04/28/1998
Edition description:
1
Pages:
366
Product dimensions:
6.00(w) x 9.00(h) x 0.90(d)

Related Subjects

Table of Contents

List of Figures
Preface
1Modeling the Constitutions of Matter1
2Analysis: The Stability of Bulk Matter15
3Mathematics: Infinite Volume Limits and Thermodynamics24
4Formalism: Constituting Bulk Matter: Solutions to the Ising Model, and Duality in Those Solutions56
5Analysis: Generic, Formal, Model-Independent Accounts of the Constitution of Matter as Philosophical101
6Formalism: Technical Devices Doing the Work of Physics129
7Physics and Mathematics: Finding the Right Mechanism and Choosing the Right Functions156
8The Physics and the Mathematics199
Appendix: Two Papers by Lars Onsager
AElectrostatic Interaction of Molecules (1939)219
BCrystal Statistics, Part I: A Two-Dimensional Model with an Order-Disorder Transition (1944)227
Notes261
References313
Index325

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