Speaker
Description
We derive an infinite family of time-dependent integral relations by performing weighted integrations of the stress-energy conservation equation in classical field theory. These relations connect weighted spatial integrals of the stress tensor to the second time derivative of weighted averages of the energy density. When this quantity vanishes, as in stationary configurations, or even only at a given instant or in a time-averaged sense, the relations reduce to integral identities for weighted spatial integrals of the stress tensor, substantially extending Derrick-type virial arguments. We then obtain their explicit form for a broad class of classical bosonic field theories whose derivative terms are quadratic in spacetime tensors. Our approach provides a direct and simple way to derive these integral identities for such models. In selected cases, the resulting relations also imply bounds on temporal contributions to the total energy. The formalism is applied to study the angular frequency of compact Q-balls and Q-shells in a CPN model with a V-shaped potential and the stability of topological solitons in the Skyrme-Maxwell theory.