# Symmetries and Paraparticles as a Motivation for Structuralism - Quantum Physics

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Abstract: This paper develops an analogy proposed by Stachel between general relativityGR and quantum mechanics QM as regards permutation invariance. Our mainidea is to overcome Pooley-s criticism of the analogy by appeal toparaparticles.In GR the equations are the solution space is invariant underdiffeomorphisms permuting spacetime points. Similarly, in QM the equations areinvariant under particle permutations. Stachel argued that this feature-atheory-s `not caring which point, or particle, is which-supported astructuralist ontology.Pooley criticizes this analogy: in QM the anti-symmetrization of fermionsand bosons implies that each individual state solution is fixed by eachpermutation, while in GR a diffeomorphism yields in general a distinct, albeitisomorphic, solution.We define various versions of structuralism, and go on to formulate Stachel-sand Pooley-s positions, admittedly in our own terms. We then reply to Pooley.Though he is right about fermions and bosons, QM equally allows more generaltypes of symmetry, in which states vectors, rays or density operators are notfixed by all permutations called `paraparticle states-. Thus Stachel-sanalogy is revived.

Author: ** Adam Caulton, Jeremy Butterfield**

Source: https://arxiv.org/