Abstract 'A Relational-Ontological and Constructivist Analysis of Neurodynamical Geometry in the Language of Quantum Field Theory'

The dynamics of neural systems form geometric structures in phase space whose analysis offers potential for
identifying and predicting neurodynamics-related disorders such as epileptic seizures.
However, current analytical approaches predominantly focus on static geometric features, while the generative processes and dynamics underlying these structures can provide valuable information.

Yet current neurodynamical analysis frameworks seldom investigate the formal generative processes underlying phase space geometries.
Meanwhile, contemporary philosophy and modern physics (field theory, noncommutative geometry) increasingly indicate that
relational-ontological primitives provide powerful foundations for modeling generative dynamics. The potential value of relational ontology
as a generative basis for understanding neurodynamical geometry formation remains largely unexplored.

We seek a formally expressive, physics- and mathematics-grounded framework capable of describing both
neurodynamical geometries and their generative processes from a relational-ontological perspective.

We propose utilizing quantum field theory (QFT) as a formal language for describing neurodynamical
geometry and its formation. QFT offers three key advantages: (1) a relational ontology that is both
philosophically and physically expressive, (2) quantum-theoretic expressiveness for describing complex
geometry formation processes, and (3) a general mathematical language for geometric emergence. As a preliminary
investigation, we employ group field theory (GFT), a specific QFT framework that describes quantum geometry
emergence from symmetry and relations using algebraic groups as ontological primitives.

This work establishes a
constructivist and relational-ontological approach to neurodynamical analysis,
demonstrating how GFT’s formalism can capture both the generative dynamics and emergent geometric structures in neural phase spaces.
We provide a conceptual bridge between quantum geometric frameworks and neuroscience, opening pathways for processual understanding of neurodynamical disorders.