What question did this study set out to answer?

This research aims to establish a connection between arithmetic properties and observables in Lagrangian quantum field theory.

March 26, 2026Open Access

The Conservation of Arithmetic as a Theorem of Lagrangian Quantum Field Theory

Key Points

This research aims to establish a connection between arithmetic properties and observables in Lagrangian quantum field theory.
Prove a conservation law related to rational prefactors in quantum field theory
Analyze twelve published results across number theory, spectral geometry, and quantum field theory
Decompose observables into a universal structure for classification
Identified constraints on rational prefactors based on prime factorization
Showed a universal structure governs the classification of observable components
Introduced the concept of Conservation of Arithmetic as a new framework

Abstract

I prove that the rational prefactors of formulas in Lagrangian quantum field theory are constrained by a conservation law governing their prime factorization. The constraint decomposes every observable into a universal structure whose components are individually classifiable. The proof assembles twelve published results spanning number theory, spectral geometry, and quantum field theory. The composition is new. I call this the Conservation of Arithmetic.

The Conservation of Arithmetic as a Theorem of Lagrangian Quantum Field Theory

Key Points

Abstract

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