ACTION–THETA–ENTROPY (ATE) THEORY — IIIb: Relativistik Ayrım Dinamiğinin Kuantum Alan Teorisi Olarak İnşası Klein–Gordon Alanının Varyasyonel Kökeni ve Kanonik Kuantizasyonu
Gerlikhan, Selçuk Gökhan
This document constitutes ATE–IIIb, the third stage of the relativistic development within the Action–Theta–Entropy (ATE) Theory series. It represents the second necessary step in the relativistic sector, following ATE–IIIa, where the Klein–Gordon equation was derived at the classical field level from a distinction-based variational principle. The purpose of ATE–IIIb is precise and deliberately limited: to demonstrate that the classical relativistic field obtained in ATE–IIIa, when subjected to standard canonical quantization, reproduces the complete and familiar structure of free relativistic scalar quantum field theory. No alternative quantization schemes are proposed, and no new quantum postulates are introduced. Rather, this volume serves as a compatibility and closure test of the ATE program against established quantum field theory. Within the ATE framework, quantization is not treated as a foundational axiom. Instead, it is applied only after a well-defined classical field structure has been established. ATE–IIIb follows this historical and conceptual ordering explicitly: first, the relativistic distinction dynamics is constructed at the classical level (ATE–IIIa); only then is canonical quantization applied. The result is the standard free Klein–Gordon quantum field theory, including its operator structure, Fock space, particle–antiparticle interpretation, conservation laws, and causal properties. A key contribution of this monograph lies not in altering quantum field theory mathematically, but in reframing its ontological interpretation. In ATE–IIIb, particles are not taken as primitive entities. Instead, they are understood as quantized modes of underlying distinction patterns. The field operators and the associated Fock space are treated as representational tools for the quantum structure of distinguishability, rather than as fundamental constituents of reality. This reinterpretation does not modify any experimental predictions, but it prepares the conceptual ground for a later, non-postulatory treatment of measurement, decoherence, and classical emergence within the ATE framework. The scope of this volume is intentionally restricted. It excludes interactions, gauge fields, screening mechanisms, and the Θ field, as well as renormalization and vacuum-energy issues. These topics are deferred to subsequent installments, where the full information-theoretic structure of ATE becomes essential. ATE–IIIb therefore completes the construction of free relativistic scalar quantum field theory, and nothing more—by design. The main text of this monograph is written in Turkish. An English version of the full manuscript is planned for a later release within the same series. It is nevertheless hoped that the universality of the canonical quantum-field-theoretic structure, together with the clear separation between classical construction and quantization, will allow interested researchers to engage with the core content despite the temporary language barrier. This Zenodo entry is intended to serve as: a definitive reference for the quantum-field-theoretic completion of the ATE relativistic program, a demonstration that ATE is fully compatible with standard free quantum field theory, and a conceptual bridge toward future volumes addressing interactions, Θ-field coupling, decoherence, and measurement.
•Dec 18, 2025•0 citations