The Conventionality of Parastatistics

Abstract

Nature seems to be such that we can describe it accurately with quantum theories of bosons and fermions alone, without resort to parastatistics. This has been seen as a deep mystery: paraparticles make perfect physical sense, so why don’t we see them in nature? We consider one potential answer: every paraparticle theory is physically equivalent to some theory of bosons or fermions, making the absence of paraparticles in our theories a matter of convention rather than a mysterious empirical discovery. We argue that this equivalence thesis holds in all physically admissible quantum field theories falling under the domain of the rigorous Doplicher–Haag–Roberts approach to superselection rules. Inadmissible parastatistical theories are ruled out by a locality-inspired principle we call charge recombination. 1 Introduction2 Paraparticles in Quantum Theory3 Theoretical Equivalence 3.1 Field systems in algebraic quantum field theory 3.2 Equivalence of field systems4 A Brief History of the Equivalence Thesis 4.1 The Green decomposition 4.2 Klein transformations 4.3 The argument of Drühl, Haag, and Roberts 4.4 The Doplicher–Roberts reconstruction theorem5 Sharpening the Thesis6 Discussion 6.1 Interpretations of Quantum Mechanics 6.2 Structuralism and haecceities 6.3 Paraquark theories