On a general theory of particles with a given total spin

Jacob Katriel, Josef Paldus, Reuben Pauncz

Abstract The well known one‐to‐one correspondence between the eigenstates of the total spin for a system of spin‐½ particles and irreducible representations of the symmetric group with up to two rows in the Young shape is the basis of interesting formal developments in quantum chemistry and in the theory of magnetism. As an explicit manifestation of this correspondence the class operators of the symmetric group are demonstrated to be expressible in terms of the total spin operator. This correspondence does not hold for higher elementary spins. The extension to arbitrary spin is investigated using Schrödinger's generalization of the Dirac identity, which expresses the transpositions in terms of two‐particle spin operators. It is shown that additional operators, which for σ = ½ reduce to the total spin operator, are needed for a complete classification. Some aspects of the formalism are developed in detail for σ = 1. In this case a classification identical with that provided by the irreducible representations of the symmetric group is obtained in terms of the eigenstates of two commuting operators, one of which is the total spin operator.

William Rarita, Julian Schwinger

Austin Blaquière

Ghi Ryang Shin, Iwo Białynicki‐Birula, Johann Rafelski A

Using the recently developed relativistic Wigner formulation for the density matrix of spin-1/2 particles, we study the $^{\mathrm{\ensuremath{\pi}}}$=1/${2}^{+}$ Coulomb-like and cavity relativistic states. One of our objectives is to understand the sharing of the total angular momentum of a quantum state between the spin and rotational degrees of freedom, arising due to the spin-orbit coupling. Another is to demonstrate that the 4\ifmmode\times\else\texttimes\fi{}4-matrix Wigner function is the appropriate generalization from the 2\ifmmode\times\else\texttimes\fi{}2 form of the nonrelativistic theory.

Nick Karayianis, Carole A. Morrison

Known results regarding the projection of total spin states from product wavefunctions involving spin-½ particles are generalized. It is shown that total spin states projected from product wavefunctions involving particles with arbitrary spin, but otherwise restricted to having either maximum or minimum z component of spin, are no more complicated in form than for the spin-½ case.

Marek Czachor