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

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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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Editorial Reviews

Taking as case studies proofs that ordinary matter is stable, and solutions to the Ising model of a phase transition, Krieger (planning, U. of Southern California) shows how the mathematical models physicists use are built upon philosophical foundations. He provides students of physics and applied mathematics with a view of the physical forest behind the mathematical trees, historians and philosophers of science with insights into how theoretical physicists go about their work, and technically advanced general readers with a glimpse into the discipline. Annotation c. by Book News, Inc., Portland, Or.
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Product Details

  • ISBN-13: 9780226453040
  • Publisher: University of Chicago Press
  • Publication date: 1/28/1997
  • Series: Cinema and Modernity Ser.
  • Edition description: 1
  • Pages: 366
  • Product dimensions: 6.00 (w) x 9.00 (h) x 1.20 (d)

Table of Contents

List of Figures
1 Modeling the Constitutions of Matter 1
2 Analysis: The Stability of Bulk Matter 15
3 Mathematics: Infinite Volume Limits and Thermodynamics 24
4 Formalism: Constituting Bulk Matter: Solutions to the Ising Model, and Duality in Those Solutions 56
5 Analysis: Generic, Formal, Model-Independent Accounts of the Constitution of Matter as Philosophical 101
6 Formalism: Technical Devices Doing the Work of Physics 129
7 Physics and Mathematics: Finding the Right Mechanism and Choosing the Right Functions 156
8 The Physics and the Mathematics 199
Appendix: Two Papers by Lars Onsager
A Electrostatic Interaction of Molecules (1939) 219
B Crystal Statistics, Part I: A Two-Dimensional Model with an Order-Disorder Transition (1944) 227
Notes 261
References 313
Index 325
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