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A powerful tool for studying the behavior of classical field theories isDerrick's theorem: one may rule out the existence of localized inhomogeneousstable field configurations (solitons) by inspecting the Hamiltonian and makingscaling arguments. For example, the theorem can be used to rule out compactdomain wall configurations for the classic $\phi^4$ theory in $3+1$ dimensionsand greater. We argue no such obstruction to constructing solitons exists inthe framework of algebraic/axiomatic quantum field theory (AQFT), and thatstates like the example given lie in topologically trivial superselectionsectors of the Hilbert space. A proof is presented making use of the relativeentropy, and the implications are explored for a few common models of scalarfields and the pure Yang-Mills theory.

Quantum Solitons in any Dimension: Derrick's Theorem v. AQFT