Trilocal structures. I. Secular equation

Abstract

The principles used with the bilocal photon are applied to the analysis of trilocal structures. From the trilocal wave equation, and the phase-space boundary condition (that the structure float on a Fermi sea filling the vacuum), a secular equation is obtained, an eighth-order polynomial in the energy of the structure. Requiring that the structure move as a particle, withw ²=k ²+m ², provides explicit expressions for two auxiliary parameters,λ andμ, to be used later in an expansion of the wave function.