Integral identities and universal relations for solitons
arxiv(2024)
摘要
We show that any nonlinear field theory giving rise to static solutions with
finite energy like, e.g., topological solitons, allows us to derive a
continuous infinity of integral identities which any such solution has to obey.
These integral identities can always be understood as being generated by field
transformations and their related Noether currents. We also explain why all
integral identities generated by coordinate transformations become trivial for
Bogomolnyi-Prasad-Sommerfield (BPS) solitons, i.e., topological solitons which
saturate a topological energy bound. Finally, we consider applications of these
identities to a broad class of nonlinear scalar theories, including the Skyrme
model. More concretely, we find nontrivial integral identities that can be seen
as model-independent relations between certain physical properties of the
solitons in such theories, and we comment on the possible connection between
these new relations and those already found in the context of astrophysical
compact objects. We also demonstrate the usefulness of said identities to
estimate the precision of the numerical calculation of soliton observables.
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