The British Journal for the Philosophy of Science

The Limits of Physical Equivalence in Algebraic Quantum Field Theory

Tracy Lupher

Published Aug 5, 2016• 3 citations

Abstract

Some physicists and philosophers argue that unitarily inequivalent representations (UIRs) in quantum field theory (QFT) are mathematical surplus structure. Support for that view, sometimes called ‘algebraic imperialism’, relies on Fell’s theorem and its deployment in the algebraic approach to QFT. The algebraic imperialist uses Fell’s theorem to argue that UIRs are ‘physically equivalent’ to each other. The mathematical, conceptual, and dynamical aspects of Fell’s theorem will be examined. Its use as a criterion for physical equivalence is examined in detail and it is proven that Fell’s theorem does not apply to the vast number of representations used in the algebraic approach. UIRs are not another case of theoretical underdetermination, because they make different predictions about ‘classical’ operators. These results are applied to the Unruh effect where there is a continuum of UIRs to which Fell’s theorem does not apply. 1 Introduction2 Weak Equivalence and Physical Equivalence3 Mathematical Overview of Algebraic Quantum Field Theory4 Fell’s Theorem and Philosophical Responses to Weak Equivalence5 Weak Equivalence in C*-Algebras and W*-Algebras6 Classical Equivalence and Weak Equivalence7 Interlude: Is Weak Equivalence Really Physical Equivalence?8 The Unruh Effect9 Time Evolution and Symmetries10 ConclusionsAppendix

DOI: 10.1093/bjps/axw017

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