Statistical operator of a system of identical interacting particles in coordinate representation. (in Ukrainian)

L. F. Blazhyjevskii

M. V. Vavrukh, Ya. Kushtay

I. O. Vakarchuk

ZOBRAENN .O. Vakarquk L~v vs~ki deravni un versitet men vana Franka, kafedra teoretiqnoÝ f ziki UkraÝna, 290005, L~v v, vul.Dragomanova, 12(Otrimano 29 grudn 1995)Otrimano novi viraz dl povnoÝ matric gustini sistemi totonih vza mod qih qastinok u koordinatnomu zobraenn u vigld dobutku matric gustini deal~nogo kvantovogo azu z perenormovano za rahunok vza mod Ý maso qastinok ta faktora, wo vrahovu m qastinkovu vza mod , ki pri niz~kih temperaturah zvodit~s do dobutku hvil~ovih funkc osnovnogo stanu bagatobozonnoÝ sistemi.

Lawrence Horwitz

The adaptation of Wigner's induced representation for a relativistic quantum theory making possible the construction of wave packets and admitting covariant expectation values for the coordinate operator x μ introduces a foliation on the Hilbert space of states. The spin-statistics relation for fermions and bosons implies the universality of the parametrization of orbits of the induced representation, implying that all particles within identical particle sets transform under the same SU (2) subgroup of the Lorentz group, and therefore their spins and angular momentum states can be computed using the usual Clebsch–Gordan coefficients associated with angular momentum. Important consequences, such as entanglement for subsystems at unequal times, covariant statistical correlations in many-body systems and the construction of relativistic boson and fermion statistical ensembles, as well as implications for the foliation of the Fock space and for quantum field theory are briefly discussed.

Robert T. Deck, Jearl D. Walker

We demonstrate that the exchange of two identical particles can be effected by a rotation of a coordinate system defined by the two particles through an angle π. It is then a consequence of the intimate connection between the generator of a space rotation and the total angular momentum operator, that the effect of the particle exchange on the ket corresponding to the physical system is dependent upon the integer or half-integer character of the particle spins. From this it can be concluded that the connection between spin and statistics that derives from the symmetry of the identical particle system under particle exchange is explained (in the most fundamental way) by the equivalence between the exchange of two identical particles and a rotation in configuration space.

H. Bacry