Equivalent Field Theories and Elementary-Particle Democracy

It is shown how one can eliminate various fields from a Lagrangian to obtain a new Lagrangian, wherein the theories obtained from the two Lagrangians are equivalent. In general the Lagrangian obtained by eliminating various fields is nonlocal. In some cases under certain requirements it can be made local. These requirements are equivalent to having the wave-function renormalization constants of the eliminated fields vanish. The results are fully illustrated by various examples. In particular, for the case of the Yukawa coupling, it is shown that if we require the Lagrangian obtained by eliminating the boson field to be local then this is equivalent to the vanishing of the wave-function renormalization constant of the boson field. From the examples it is surmised that the creation of elementary-particle democracy is achieved by eliminating various fields from the Lagrangian and requiring all the final self-interacting Lagrangians to be local.