R-layer Mode Theory LXI: Quantum Field-Theoretic Structure and Collision-Induced Oscillations in the R-layer

Volume LXI develops the quantum field-theoretic extension of the R-layer Mode Theory (RLMT), establishing the continuous-limit framework in which layered mode structures become fully dynamical quantum fields. Building on the algebraic foundations of Appendix X and the geometric infrastructure of Appendix Y, this volume formulates the QFT-level action, propagators, and interaction rules governing AUP, MUP, and CUP modes in the continuum R-layer. The construction clarifies how discrete layer indices, projection operators, and inter-layer correspondences lift to field-theoretic objects with well-defined transformation and correlation properties. A central result of this volume is the derivation of collision-induced oscillations: coherent mode-mixing phenomena that arise when layered excitations interact through the R-layer’s intrinsic coupling structure. These oscillations provide a dynamical signature of the layered geometry and offer a bridge between the microscopic mode algebra and emergent macroscopic behavior. The volume presents the general mechanism, the effective field equations, and the conditions under which oscillatory behavior becomes resonant, suppressed, or decohered. Volume LXI serves as the foundational QFT reference for RLMT, supplying the continuous-limit formalism required for cosmological, quantum-informational, and geometric applications developed in later volumes. Together with Appendices X and Y, it completes the core mathematical infrastructure of the theory and establishes the framework for analyzing dynamical processes within the R-layer.