Abstract:

A remarkable feature of quantum theory is that particles with identical intrinsic properties must be treated as indistinguishable if the theory is to give valid predictions. For example, our understanding of the structure of the periodic table hinges on treating the electrons in multi-electron atoms as indistinguishable. In the quantum formalism, indistinguishability is expressed via the symmetrization postulate, which restricts a system of identical particles to the set of symmetric states ('bosons') or the set of antisymmetric states ('fermions'). However, the precise connection between particle indistinguishability and the symmetrization postulate has not been established. There exist a number of variants of the postulate that appear to be compatible with particle indistinguishability, and a well-known derivation of the postulate implies that its validity depends on the dimensionality of space. These variants leave open the possibility that there exist elementary particles, such as anyons, which violate the symmetrization postulate.

In this talk, we show that the symmetrization postulate can be derived on the basis of the 'indistinguishability postulate' [1].  This postulate establishes a functional relationship between the amplitude of a process involving indistinguishable particles and the amplitudes of all possible transitions when the particles are treated as distinguishable. The symmetrization postulate follows by requiring consistency with the rest of the quantum formalism. The key to the derivation is a strictly informational treatment of indistinguishability which prohibits the labeling of particles that cannot be experimentally distinguished from one another. The derivation implies that the symmetrization postulate admits no natural variants. In particular, the existence of anyons as elementary particles is excluded.

[1] "Informational Approach to Identical Particles in Quantum Theory", http://arxiv.org/abs/1309.0478

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