Identity, Superselection Theory, and the Statistical Properties of Quantum Fields

Abstract

The permutation symmetry of quantum mechanics is widely thought to imply a sort of metaphysical underdetermination about the identity of particles. Despite claims to the contrary, this implication does not hold in the more fundamental quantum field theory, where an ontology of particles is not generally available. Although permutations are often defined as acting on particles, a more general account of permutation symmetry can be formulated using superselection theory. As a result, permutation symmetry applies even in field theories with no particle interpretation. The quantum mechanical account of permutations acting on particles is recovered as a special case.

Infinite Scale Skepticism: Probing the Epistemology of the Limit of Infinite Degrees of Freedom and Hilbert Space Non-Uniqueness

“…Indeed, this work by Landsman, Kijowski and Rudolf, hints that the inequivalent representations employed in the Doplicher-Haag-Roberts (DHR) theory of superselection, one of the crown jewels of algebraic QFT, spring from quotienting out a symmetry rather than speculative assumptions about the extreme ultraviolet and infrared. 28 In that case, philosophical work employing this formalism (for instance, Halvorson and Müger [2007]; Baker and Halvorson [2010]; Baker [2013]) would escape unscathed from the worries about the epistemic status of the limit of infinite degrees of freedom raised in this paper.…”

Scientific Realism Made Effective

“…There have been arguments presented in its favor -in particular, arguments for ignoring EFTs in favor of attempting to extract ontological information by answering the nested counterfactual given above (for example, [Fraser, 2009], [Kuhlmann, 2010], [Fraser, 2011], or [Baker, 2013]). However, these arguments reveal a third vice of adhering to Standard Interpretive methodology: it can generate conclusions we have good reason to believe (at best) non sequiturs, and (at worst) false.…”