On the existence of finite-energy lumps in classic field theories

TL;DR

This paper investigates the conditions under which finite-energy, time-dependent classical lumps can exist in certain field theories, using a generalized virial theorem to establish restrictions and bounds.

Contribution

It introduces a generalized virial theorem that constrains the existence of finite-energy lumps in classical field theories and derives energy bounds for simple models.

Findings

Finite-energy lumps are restricted by the virial theorem.

Bounds on energies are derived for specific Lagrangians.

Existence of non-trivial lumps depends on model parameters.

Abstract

We show how the existence of non-trivial finite-energy time-dependent classical lumps is restricted by a generalized virial theorem. For simple model Lagrangians, bounds on energies follow.