On a Theory of Particles with Half-Integral Spin

A. Bağcı

I. M. Ternov, Vladimir A Bordovitsyn

The basic propositions of the classical spin theory are considered. The classical equations of motion of a point particle with half-integral spin are developed. An analysis of the spin equations is given.

R. Potier

L. de la Peña-Auerbach

The stochastic theory of quantum mechanics is further developed to include the problem of extended rigid particles, thus allowing the introduction of spin. It is demonstrated that the stochastic equations for the system's center of mass give rise to a generalized Schrödinger equation for integral or half-integral spin; in the particular case of spin ½, upon elimination of the internal variables, Pauli's equation is obtained. A formal simplified relativistic extension of the theory is worked out and shown to lead to Dirac's equation in the case of spin ½ and for a gyromagnetic ratio equal to 2; in the case of arbitrary spin, the theory gives an equation of the Feynman-Gell-Mann type.

William G. Harter, Narciso dos Santos

A geometrical construction by Hamilton is used to simplify the quantum mechanics of half-integral spin. A slide rule is described which can be used to (a) compute products of half-integral or integral spin rotation operators, (b) convert between the Euler-angle and ’’axis-angle’’ rotation operator parameters, and (c) calculate the time evolution of a spin-1/2 state for a constant Hamiltonian operator. A type of nomogram is developed which suggests ways to simplify the ’’double-group’’ theory of half-integral spin in molecular point symmetry, as well as the ’’ordinary’’ group theory for integral spin systems. Cubic and icosahedral symmetry group characters are derived for half-integral spin operators.