An Informational Approach to Identical Quantum Particles

Philip Goyal ( University at Albany — Department of Physics )

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. 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 physical basis and range of validity of the symmetrization postulate has not been established, and variants have been proposed. For example, a well-known topological derivation of the symmetrization postulate implies that its validity depends on the dimensionality of the space in which the particles move (Laidlaw–DeWitt and Leinaas–Myrheim). This variant leaves open the possibility that identical particles are generically able to exhibit so-called anyonic behavior (that interpolates between fermionic and bosonic behavior) in two spatial dimensions.

In this talk, I outline how the symmetrization postulate can be derived by strictly adhering to the informational requirement that particles which cannot be experimentally distinguished from one another are not labelled. The key novel postulate is the operational indistinguishability postulate, which posits that the amplitude of a process involving several indistinguishable particles is determined by the amplitudes of all possible transitions of these particles when treated as distinguishable. The symmetrization postulate follows by requiring consistency with the rest of the quantum formalism as expressed in terms of Feynman’s path-amplitude framework. The derivation implies that the symmetrization postulate admits no natural variants. In particular, the possibility that identical particles generically exhibit anyonic behavior in two dimensions is excluded.

This talk is based partially on the paper "Informational Approach to the Quantum Symmetrization Postulate”, NJP, 2015; available via open access at http://iopscience.iop.org/article/10.1088/1367-2630/17/1/013043