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June 28, 2026Open Access

Hamilton's Principle, Feynman's Path Integral, and the Action Quantum h = 2πℏ as Capacity-Rotor Theorems: A Parameter-Free Derivation from QTT Axioms A1--A7U

Key Points

This work aims to derive Hamilton's principle, Feynman's path integral, and the action quantum as theorems within Quantum Traction Theory.
Developed QTT native forms of the continuum path integral and action quantum.
Utilized axioms A1 to A7U to construct theoretical frameworks.
Incorporated established rules such as Planck-Einstein and de Broglie to illustrate relationships.
Demonstrated the action quantum as h=2πℏ through the closure theorem.
Established multiple quantum rules as projections of the same dial-closure statement.
Introduced new standards and definitions within the context of Quantum Traction Theory.

Abstract

Hamilton's Principle, Feynman's Path Integral, and the Action Quantum as QTT Capacity-Rotor Theorems Version: 2. 02 First public release: 9 May 2026 Current release: 26 June 2026 Concept DOI: 10. 5281/zenodo. 20098143 Author: Ali Attar Website: quantumtraction. org This paper develops Hamilton's stationary-action principle, Feynman's path integral, and the action quantum \ (h=2\) as Quantum Traction Theory (QTT) capacity-rotor theorems. The central source claim is that a physical history advances a real \ (J\) -dial by \ d=dS, \ so the laboratory path-integral weight is not introduced as a primitive complex phase. It is the access shadow of a real source rotor: \ RJ () =\, I+\, J, J²=-I, J^=-J. \ The continuum path integral is written in QTT-native form as \ KJ (b, a) = ₇_ ₀₇ₔ (a, b) D ₀₆\, RJ\! (S ₓ₎ₓ[). \] The action quantum follows from A4 action-angle transport plus A7/A7U closure: \ S ₎₍₄\ ₑ₄ₕ₎₋ₔₓ₈₎₍ = 2 h. \ The Planck--Einstein rule \ (ET=h\), de Broglie rule \ (p=h\), Bohr--Sommerfeld loop rule \ (p\, dq=nh\), and flux-quantization rule \ (q=nh\) are treated as projections of that same dial-closure statement. Version 2. 02 does not change the theorem rail of v2. 01. It is an onboarding, provenance, and audit release. It adds the corpus-wide QTT Onboarding standard, plain definitions of first-use QTT terms, the first public release date, an early scale-status/no-circularity note for \ (/A\), a familiar recovery route, early falsifiers, an Artian's Universe statement, website deep anchors, a load-bearing axiom/concept map, and concept-DOI-only citation cleanup. Main status labels: GREEN: STATIONARY-ACTION-RECOVERY-IN-LOW-ENERGY-SHADOW GREEN: REAL-J-ROTOR-HISTORY-WEIGHT-DERIVED-FROM-QTT-AXIOM-CHAIN GREEN: ACTION-QUANTUM-CLOSURE-THEOREM-H-EQUALS-2PI-HBAR GREEN: STANDARD-CLOSURE-RULES-RECOVERED-AS-PROJECTIONS YELLOW: SECTOR-SPECIFIC-A7U-RESIDUALS-REQUIRE-PRINTED-BUNDLE-GRAPH Related QTT anchors: Main book: 10. 5281/zenodo. 17527179 The Artian Hamiltonian Framework: 10. 5281/zenodo. 20484906 The Artian Lagrangian Framework: 10. 5281/zenodo. 20657182 Observation as Access: 10. 5281/zenodo. 20114403 From Rotor to Wavefunction: 10. 5281/zenodo. 20119662 Corpus Tree: quantumtraction. org/doi-map/ Derivation Atlas: quantumtraction. org/derivation-atlas/ Lexicon: quantumtraction. org/lexicon/ Included files: PDF paper, Version 2. 02 Complete reconstruction ZIP containing LaTeX source, local load-bearing style module, Zenodo description HTML, render audit, metadata, and hashes

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