In the considerable physical and philosophical literature,1 ‘indistinguishability’, and the related concept of ‘identicality’, are used in many ways, and in the resulting confusion the logical relations between the various notions are often obscured, with unfortunate consequences. This article will use them in the following senses, which are most useful and (likely) common:
Particles are identical if they share in common all their constant properties, such as mass, charge, spin and so on: that is, if they agree in all their state-independent or intrinsic properties. Particles are indistinguishable if they satisfy the indistinguishability postulate (IP). This postulate states that all observables O must commute with all particle permutations P: [O, P] = 0. Put informally, the IP is the requirement that no expectation value of any observable is affected by particle permutations.
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Huggett, N., Imbo, T. (2009). Indistinguishability. In: Greenberger, D., Hentschel, K., Weinert, F. (eds) Compendium of Quantum Physics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-70626-7_97
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