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MP: Fachverband Theoretische und Mathematische Grundlagen der Physik

MP 14: Mathematische und Philosophische Grundlagen (gemeinsam mit AG Phil)

MP 14.1: Vortrag

Donnerstag, 19. März 2015, 09:30–10:00, HFT-FT 101

Classical Field Theory and Intertheoretic Reduction — •Samuel C. Fletcher — Munich Center for Mathematical Philosophy, LMU Munich, Germany

In 1986, Ehlers set out a program on how to understanding the approximative relationships between different physical theories. However, he essentially only investigated the case of classical and relativistic spacetime theories, which have a number of special features that distinguish them from broader classes of physical theories. To what extent, then, can the Ehlers program be successful? I outline some of the challenges facing the program's generalization and argue that they can largely be overcome for classical gauge theories, i.e., theories described by connections on principal bundles, once the program is understood geometrically.

The general strategy is to cast the successfully treated case of general relativity and Newtonian gravitation - really, the geometrized version thereof, Newton-Cartan theory - as a reduction between two gauge theories. Under this guise, one can understand its relation to the theory of group contraction, to associated vector bundles representing matter fields, and to different notions of convergence encoding different ways the matter fields of the limit theory may approximate those of the limiting theory.