Constitutions of Matter: Mathematically Modeling the Most Everyday of Physical Phenomenaby Martin H. Krieger
Pub. Date: 01/28/1997
Publisher: University of Chicago Press
Using two tours de force of
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-Krieger uncovers the philosophical roots of the mathematical models of these phenomena. He shows not only how physicists believe the natural world is structured, but also how they make those conclusions.
Krieger's lucid discussions will help readers to appreciate the larger physical issues behind the mathematical detail of modern physics and gain deeper insights into how theoretical physicists work. Constitutions of Matter is a rare, behind-the-scenes glimpse into the world of modern physics.
Table of Contents
1: Modeling the Constitutions of Matter
2: Analysis: The Stability of Bulk Matter
3: Mathematics: Infinite Volume Limits and Thermodynamics
4: Formalism: Constituting Bulk Matter: Solutions to the Ising Model, and Duality in Those Solutions
5: Analysis: Generic, Formal, Model-Independent Accounts of the Constitution of Matter as Philosophical
6: Formalism: Technical Devices Doing the Work of Physics
7: Physics and Mathematics: Finding the Right Mechanism and Choosing the Right Functions
8: The Physics and the Mathematics
Appendix: Two Papers by Lars Onsager
A: Electrostatic Interaction of Molecules (1939)
B: Crystal Statistics, Part I: A Two-Dimensional Model with an Order-Disorder Transition (1944)
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