Fock Space and the Theory of Infinity: A Comparative Analysis of Foundations and Frameworks

Ryan E. S. Charmley

Published Dec 28, 2025• 0 citations

Abstract

This paper compares two frameworks that confront “infinity” in sharply different ways: (i) Fock space, the graded Hilbert-space construction underlying second quantization and quantum field theory, which accommodates superpositions across particle-number sectors; and (ii) the Theory of Infinity (TOI), an ontological/computational program in which infinity is taken as a primitive and finite “contexts” are generated through iterative symmetry operations. We focus on three comparative axes: (a) how variable cardinality is represented, (b) how symmetry is implemented, and (c) how invariants constrain permissible structure and dynamics. Although the two frameworks are not mathematically equivalent, both employ a graded decomposition (particle-number sectors in Fock space versus a nested context lattice in TOI) and treat invariants as structuring constraints. We conclude by identifying robust analogies (graded structure, invariants, refinement) and the principal divergences (linear operator-algebraic versus nonlinear iterative dynamics; potential/sectoral versus ontological infinity).

DOI: 10.5281/zenodo.18078855

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