Atomic, Molecular, and Optical Physics within Global Realism: Finite-Core Structure, Correlated Spectroscopy, Nonadiabatic Molecular Dynamics, and Controlled Light–Matter Interaction

We formulate a unified framework for atomic, molecular, and optical physics based on three physical axioms: finite microscopic localization, the physical reality of a single spacetime–vacuum substrate, and persistent causal source–response coupling. Wave functions, orbitals, Slater determinants, Fock states, and field operators are treated strictly as mathematical representations rather than additional physical substances. Starting from self-adjoint finite-core Hamiltonians, we derive atomic bound states, antisymmetric many-electron structure, Hartree–Fock, configuration-interaction, perturbative, coupled-cluster, and response formulations within a common operator framework. Riesz and Feshbach projections provide controlled effective Hamiltonians, while explicit spectral gaps, operator norms, residual bounds, and failure criteria delimit all approximations. The atomic sector develops relativistic structure, fine and hyperfine interactions, isotope shifts, Zeeman, Paschen–Back, and Stark effects, reduced transition amplitudes, absolute radiative rates, lifetimes, branching fractions, forbidden transitions, continuum response, and correlated uncertainty propagation. The molecular sector begins with the translationally reduced electron–nuclear Hamiltonian and derives Born–Huang channel equations, nonadiabatic couplings, rovibrational dynamics, conical intersections, geometric phases, dissociation channels, and detector-level molecular spectra. The optical sector derives minimal-coupling and multipolar representations, Rabi and Ramsey dynamics, Raman processes, STIRAP, electromagnetically induced transparency, master equations, cavity and waveguide response, photon correlations, and calibrated measurement records. Controlled limits are specified by dimensionless parameters and norm-bounded remainders. Instrument response, collision effects, nuclear structure, standard self-energy corrections, finite-core contributions, and candidate historical response are maintained in separate ledgers. Shared parameters are tested across atomic spectra, molecular observables, coherent control, linewidths, scattering, and detector records through covariance-aware cyclic holdout procedures. Standard AMO theory is recovered as a required limiting representation; its empirical success is not reinterpreted as independent evidence for a new ontology. **Keywords** Atomic structure; molecular physics; quantum optics; finite-core Hamiltonians; self-adjoint operators; Riesz projection; Feshbach projection; many-body theory; atomic spectroscopy; nonadiabatic dynamics; geometric phase; light–matter interaction; controlled approximations; uncertainty quantification; global realism.