On the Emergence of Fermionic Statistics from Solitons in Chronon Field Theory

We derive the emergence of fermionic spin-statistics behavior from first principles within Chronon Field Theory (CFT), a background-independent framework in which time is modeled as a dynamical, future-directed, unit-norm timelike vector field Φµ (x). In this theory, matter arises not as quantized excitations of fundamental fields, but as topologically stable solitons of the Chronon field, characterized by a winding number w ∈ π3(S^3 ) = Z. Focusing on the minimal nontrivial sector w = 1, we show that such solitons naturally transform as spin- 1/2 objects under spatial rotations and exhibit Fermi–Dirac statistics under exchange. Our analysis proceeds by constructing the soliton moduli space M1, identifying its nontrivial topology, and building the associated spin bundle over which fermionic wavefunctions are defined. We further analyze the unordered two-soliton configuration space, showing that its fundamental group enforces antisymmetric exchange statistics. These results are independently confirmed via a path integral approach, where exchange trajectories accumulate a Berry phase of π. The spin-statistics connection thus emerges from the causal and topological structure of time itself, without reliance on operator axioms or second quantization. Chronon Field Theory thereby offers a geometric and background-independent foundation for quantum matter.