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.
It is shown that spatially localized singularity-free particlelike solutions exist for Lorentz-covariant complex scalar field theories with minimal gauge-invariant electromagnetic coupling, a positive-definite energy density, and suitably prescribed nonlinear self-interaction. Such a theory provides a perfectly consistent structural model on the classical level for a charged elementary particle of finite positive energy.
The Galilean invariance of nonrelativistic laws is reviewed with particular attention given to the transformation properties of field-theoretic quantities. It is then shown that Galilean-invariant nonrelativistic laws generally manifest a broader covariance, the laws retaining their form under coordinate transformations to noninertial frames which move with arbitrary accelerative translational motion (without rotation) with respect to inertial frames.
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