The Interpretation of Contemporary Gauge Theories

University Of Arizona, Tucson AZ

Investigators

Abstract

SES 0216918 -- The Interpretation of Contemporary Gauge Theories Richard Healey, University of Arizona The proposed project is to analyze the conceptual foundations and implications of gauge theories in physics with a view to answering the central interpretative question: What is the world like if a gauge theory is true of it? Gauge theories are of fundamental importance to contemporary physics. Three of the four basic physical interactions acknowledged today are currently best described by quantized gauge theories, and the concept of gauge has also been fruitfully applied to the fourth, gravity. But the conceptual foundations and implications of gauge theories remain unclear. It is up to the philosopher of science to analyze these and make them clear to scientists, philosophers and interested laymen who seek a deeper understanding of the content and significance of contemporary physics. Besides contributing to the philosophy of science, it is hoped that conceptual clarifications resulting from the proposed research will broaden the education and facilitate the thinking of theoretical physicists in their attempts to go beyond the Standard Model of elementary particles, and to arrive at a successful quantum theory of gravity. Previous research by the proposed PI has yielded an interpretation of a class of classical gauge theories, including electromagnetism. The conclusion was that these theories are best understood as ascribing properties not simply at each point of space at each instant, but rather directly on closed paths in space-time. Arguments for this conclusion rest on an analysis of the behavior of quantum-mechanically described particles interacting with a classical gauge field. Do similar conclusions emerge from a fully quantum mechanical analysis which treats both "particles" and interactions by means of quantized fields? Recent loop-space quantizations of Yang-Mills fields suggest this may be so. A major goal of the project is to pursue this suggestion, and to explore the implications of this kind of non-locality for natural philosophy. The project then investigates the possibility of an interpretation of loop-space quantum gravity as a gauge theory that attributes properties non-locally on closed paths in space-time. Smolin (2001) takes the loops themselves as basic, with space-time emerging from appropriate structures of loops in some classical limit. This suggests a more radical form of non-locality in which properties are ascribed to objects more fundamental than space-time (though space-time itself emerges as an approximate construction out of such objects). The project will evaluate the coherence, credibility, and implications of this suggestion. The project is to be conducted over the course of two summers as well as the academic year 2002-2003. The proposed PI intends to accept an invitation to spend several months during 2003 in London, England as a Visiting Fellow of the Centre for the Philosophy of the Natural and Social Sciences at the London School of Economics. This should facilitate consultations with both philosophers and physicists interested in the topic of the proposed research.