Recursive Algebra in Extended Integrated Symmetry: An Effective Framework for Quantum Field Dynamics

We propose the Extended Integrated Symmetry Algebra (EISA) as a purely exploratory effective field theory (EFT) model aimed at probing potential avenues for unifying quantum mechanics and general relativity, supplemented by the Recursive Info-Algebra (RIA) extension that incorporates dynamic recursion via variational quantum circuits (VQCs) designed to minimize Von Neumann entropy and fidelity losses. Within this framework, EISA's triple superalgebra AEISA = ASM ⊗ AGrav ⊗ AVac integrates Standard Model symmetries, gravitational norms, and vacuum fluctuations, while RIA optimizes information loops to facilitate emergent quantum field dynamics without invoking extra dimensions. Processes such as transient virtual pair creation and annihilation are coupled to a scalar field ϕ in a modified Dirac equation, which may potentially contribute to curvature sourcing and phase transitions. The model's mathematical self-consistency is rigorously verified through super-Jacobi identities, guaranteeing algebraic closure across symmetry sectors. This approach offers a novel blend of quantum information principles and algebraic structures, wherein recursive optimization could drive the emergence of physical laws from fundamental symmetries, providing a computational tool via variational quantum circuits to investigate vacuum stability and entropy minimization in extended symmetry spaces. Ultimately, this work lays a foundational, phenomenological basis for exploring quantum-gravitational effects through a unified algebraic lens that derives dynamics from information-theoretic optimization, suggesting alternative paths for studying quantum gravity and emergent spacetime while remaining fully compatible with established mainstream physics at low energies.