Two-particle spin states and generalized Bell’s inequalities

A new formalism for calculation of the spin correlation magnitude is developed. In this approach, the mean value of an operator acting in the four-dimensional space of two-particle spin states has the form of a scalar product of vectors defined in the three-dimensional direction space. A complete description of the two-particle spin states satisfying Bell inequalities is given in this formalism. It is shown that these states include both factorable and entangled states.