Particlelike Solutions to Nonlinear Complex Scalar Field Theories with Positive-Definite Energy Densities

Abstract

It is shown that a self‐interacting complex scalar field theory with a positive‐definite energy density can admit spatially localized singularity‐free particlelike solutions. A condition on the self‐interaction energy density, sufficient to guarantee the existence of such solutions, is that its derivative should be nonincreasing and not identically constant as the squared absolute value of the field increases from zero.