Distinguishable- and indistinguishable-particle descriptions of systems of identical particles

The problem of distinguishability of identical particles is considered from both experimental and theoretical points of view. It is argued that distinguishability has to be defined relative to a definite set of experiments and that the criterion by which the particles are distinguished should be specified. Failure to do so may cause mismatching between theory and experiment. On the theoretical level a distinction is made between indexed- and unindexed-particle theories, indices being unobserved intrinsic properties of the particles. A field theory of indexed particles is constructed and shown to be equivalent to the second quantization formalism, which is an unindexed-particle theory.