Relativistic Wave Equations with Maximum Spin Two

Abstract

The relativistic wave equations with maximum spin 2 in the canonical form are analyzed under the assumption that each matrix involved is a direct sum of two mutually commutable Duffin-Kemmer operators. Five independent sets of tensor equations are established by algebraic procedures and each set of equations is further reduced to several simple sets of equations, each corresponding to definite values of mass and spin. Physical consequences of the theory are discussed. Two mass values are possible, one being twice as large as the other, and possible values of spin are 2, 1 and 0. The field with spin 2 is of Pierz-Pauli type. But among the fields with spin 1 we find some ones governed by the equations different from the usual ones of the vector meson. The total energy of the whole :field is not positive definite, the conttibutions of the parts with lower and higher mass values being positive and negative respectively.