Quantum Composite Photons in the Field–Wave Sector of the Locked Skyrme Model - Paper 8

This paper takes the first quantum step in the locked SU(2) Skyrme program, quantizing the Field-Wave sector and showing that the composite emergent Maxwell field behaves as a quantum Maxwell field in the semiclassical regime. We quantize the linearized Skyrme field (pion fields) and define F^{em}{μν}(x) as a Wick-ordered composite operator built from pion gradients, preserving the composite picture where photons emerge from the underlying Skyrme field rather than being fundamental. On semiclassical Field-Wave states sharply peaked around classical solutions, we prove that expectation values of F^{em}{μν}(x) reproduce the classical emergent Maxwell field up to small corrections, and that the vacuum Maxwell equations hold in expectation up to controllable errors. The key result is that this composite operator, built strictly from pion fields, behaves as a quantum Maxwell field in its semiclassical Field-Wave regime without requiring a separate photon Fock space or fundamental gauge field. This establishes a quantum version of the emergent electrodynamics where photons are composite excitations of the single continuous Skyrme field U(x). This work is part of a program to realize both matter (Skyrmions) and radiation (Maxwell waves) as different configurations of a single continuous SU(2) Skyrme field.