The symmetrization postulate (SP) that states of more than one identical particle are either symmetric or antisymmetric under permulations is studied from the theoretical and experimental points of view. The theoretical analysis is carried out within the framework of particle quantum mechanics; the field-theory approach to identical particles using Bose, Fermi, para-Bose and para-Fermi quantization is not considered in this article. Particles not obeying SP can be accommodated in quantum mechanics, provided some modifications are made in the usual quantum-mechanical formalism. The main modification is to replace the usual ray by a many-dimensional "generalized ray" as the representative of a physical state. The properties of one-body measurements of systems having several identical particles are discussed, and the unobservability in such measurements of interferences between states having different irreducible permutation symmetries is pointed out. The condition of indistinguishability of identical particles is formulated precisely, and is analyzed both for interactions which conserve particle number and for general interactions which do not. For such general interactions, with the additional assumptions of time-reversal invariance and of coherence of the states having given values of charge, baryon number, and lepton number, it is shown that there is an absolute selection rule forbidding transitions between states ${\mathcal{F}}^{\ifmmode\times\else\texttimes\fi{}}$ which contain any number of particles of species which obey SP but at most one particle of a species not obeying SP, and states which violate SP. Since only states in ${\mathcal{F}}^{\ifmmode\times\else\texttimes\fi{}}$ are now avaiable as initial states of experiments, this selection rule forbids production of SP-violating states in any experiment which is feasible at present. Because of this, presently proposed experimental tests of SP are in fact tests of the quantum-mechanical description of identical particles together with time-reversal invariance and coherence of states in a given superselecting sector. The inclusion of internal variables, such as isospin, for particles violating SP is discussed. A comprehensive discussion is given of direct experimental tests of the SP selection rules. Such tests are more difficult to perform than appears at first sight, because in many cases the indistinguishability of identical particles or the conservation laws already imply the consequences of SP. Criteria for valid tests of SP are given. Several different types of tests are described, with illustrative examples of each. A survey is given of the direct experimental evidence for SP for the various particles. The Fermi character of electrons and positrons and of nucleons is accepted, as is the Bose character of photons. There is good evidence for the Bose nature of pions, especially from the absence of $2\ensuremath{\pi}$ decay of
K20. There is no direct evidence for the statistics of
K, $\ensuremath{\Lambda}$, $\ensuremath{\Sigma}$, $\ensuremath{\Xi}$, or $\ensuremath{\mu}$. Feasible tests are proposed for the statistics of
K and of those hyperons which have an asymmetric decay; but no such tests were found for the other hyperons or for $\ensuremath{\mu}$.
An accurate test of the symmetrization postulate of quantum mechanics has been performed on the spin-0
16O nuclei, by looking for transitions in the
CO2 spectra involving states which are antisymmetric in the exchange of the nuclei. Using high-sensitivity laser spectroscopy, a bound of $2.1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}9}$ has been set to a possible violation of such postulate, with an improvement of more than 2 orders of magnitude with respect to the previous limit.
We propose a scheme for testing the small violations of the symmetrization postulate (SP) for photons in cavity QED. In the scheme, a degenerate Λ-type three-level atom is sent through a cavity field initially in a q -deformed coherent state. After an appropriate interaction time, the atom is measured by a state-selective detector. The probability that the atom makes a transition from one of the lower states to the other characterizes the violation of the SP. In the scheme, only one atom is required and classical fields are unnecessary, which is prior to the previous schemes.
We propose a test for small violations of the symmetrization postulate (SP) for microwave photons using Rydberg atoms in cavity QED. The method requires sequences of two properly prepared and manipulated atoms interacting with the cavity field in a dispersive manner. The cavity field is assumed to be prepared in a q-deformed coherent state. In the case when the SP holds, a sequence of two atoms would always be detected in the same state, but a small violation yields a nonzero probability that the second atom will be found in a different state. We make some estimates of the feasibility of the proposed experiment.
We investigated the spectrum of the
16O2 molecule by high-sensitivity laser spectroscopy and searched for transitions involving states which are antisymmetric under the exchange of the nuclei. These states are forbidden by the symmetrization postulate of quantum mechanics. This is the first reported experiment to test the symmetrization postulate for integer-spin particles to high precision. Our data set an upper limit of $5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}7}$ to a possible violation of this postulate.