Paper VII — Variable Particle Number and Field-Theoretic Extension DescriptionThis paper generalizes the ordered-dynamics framework to systems with variable particle number, enabling a natural transition to field-theoretic descriptions. Creation and annihilation processes arise from changes in operational record structure rather than from imposed second-quantization rules. The results provide an operational route to quantum field theory within the Ordered-Dynamics Reconstruction Program. Keywordsquantum field theory; variable particle number; second quantization; operational dynamics; foundations of QFT
The approximations of classical mechanics resulting from quantum mechanics are richer than a correspondence of classical dynamical variables with self-adjoint Hilbert space operators. Assertion that classical dynamic variables correspond to self-adjoint Hilbert space operators is disputable and sets unnatural limits on quantum mechanics. Well known examples of classical dynamical variables not associated with self-adjoint Hilbert space operators are discussed as a motivation for the realizations of quantum field theory that lack Hermitian field operators but exhibit interaction.