Topological–Historical Particle Quantum Mechanics: Finite Carriers, Causal Histories, and Many-Particle Dynamics

This monograph develops a particle-first framework for many-particle quantum mechanics based on finite topological carriers, their actual causal histories, and a physical spacetime–vacuum substrate. The construction retains three physical axioms: microscopic ontic definiteness with finite localization, the physical reality of the substrate, and persistent causal source–response coupling. Euclidean self-return is treated as a geometric condition of a specified substrate realization rather than an additional matter axiom. The framework connects covariant parent dynamics and finite-energy carrier configurations to stratified many-particle configuration spaces, joint histories, preparation measures, probability currents, and conditional phase and Hilbert-space representations. Fixed- and variable-particle-number dynamics are formulated within a common sector-resolved description. Particular attention is given to finite-core interactions, historical memory, collision-induced changes in carrier decomposition, scattering, bound states, resonances, creation, annihilation, and decay. The manuscript presents scattering constructions for specified short-range interaction classes, together with multichannel and three-cluster formulations. Exchange statistics, entanglement, measurement records, kinetic reduction, and collective phenomena are examined as related aspects of the enlarged carrier–substrate dynamics. Local fields, propagators, diagrammatic expansions, and other effective computational tools are introduced downstream as representations on explicitly restricted domains. Their use does not assign independent ontic status to operator-valued fields or internal diagram lines. Mathematical results, physical-realization assumptions, numerical calculations, and empirical validation are distinguished throughout. A complete computational replacement for quantum field theory is not claimed: model-specific interaction kernels, reproducible many-particle calculations, and quantitative comparisons between particle and effective-field descriptions remain central tasks. Owing to the integration of material developed through successive stages of research and revision, the present draft contains some uneven organization, repetition, and discontinuities in its logical presentation. A simplified and reorganized version, with a clearer logical sequence and more concise exposition, is planned for subsequent publication. Keywords Finite topological carriers; causal histories; many-particle quantum mechanics; stratified configuration spaces; historical memory; collision and scattering; variable particle number; quantum reactions; exchange statistics; effective field representations.