Indistinguishability in general probabilistic theories

• URL: http://arxiv.org/abs/2412.20963v1
• Date: Mon, 30 Dec 2024 14:00:17 GMT
• Title: Indistinguishability in general probabilistic theories
• Authors: John H. Selby, Victoria J. Wright, Máté Farkas, Marcin Karczewski, Ana Belén Sainz,
• Abstract summary: We lay out a path for the study of indistinguishable particles in general probabilistic theories (GPTs) In the first approach we define different types of indistinguishable particle by the orbits of symmetric states under transformations. In the diagrammatic approach, we find a decomposition of the symmetrised state space using two key constructions from category theory. In both cases for pairs of indistinguishable particles in quantum theory we recover bosons and fermions.
• Score: 1.1650821883155187
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• Abstract: The existence of indistinguishable quantum particles provides an explanation for various physical phenomena we observe in nature. We lay out a path for the study of indistinguishable particles in general probabilistic theories (GPTs) via two frameworks: the traditional GPT framework and the diagrammatic framework of process theories. In the first approach we define different types of indistinguishable particle by the orbits of symmetric states under transformations. In the diagrammatic approach, we find a decomposition of the symmetrised state space using two key constructions from category theory: the biproduct completion and the Karoubi envelope. In both cases for pairs of indistinguishable particles in quantum theory we recover bosons and fermions.

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