Mathematics and reality: Two notions of spacetime in the analytic and constructionist views of gauge field theories

Philosophy of Science 67 (3):494 (2000)
Abstract
This paper presents two interpretations of the fiber bundle formalism that is applicable to all gauge field theories. The constructionist interpretation yields a substantival spacetime. The analytic interpretation yields a structural spacetime, a third option besides the familiar substantivalism and relationalism. That the same mathematical formalism can be derived in two different ways leading to two different ontological interpretations reveals the inadequacy of pure formal arguments
Keywords Spacetime  Field Theory
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DOI 10.1086/392840
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