Quantum Fields in Action

Jianhao M. Yang

Abstract Recently it is shown that the non-relativistic quantum formulations can be derived from an extended least action principle Yang (2023). In this paper, we apply the principle to massive scalar fields, and derive the Schrödinger equation of the wave functional for the scalar fields. The principle extends the least action principle in classical field theory by factoring in two assumptions. First, the Planck constant defines the minimal amount of action a field needs to exhibit in order to be observable. Second, there are constant random field fluctuations. A novel method is introduced to define the information metrics to measure additional observable information due to the field fluctuations, which is then converted to the additional action through the first assumption. Applying the variation principle to minimize the total actions allows us to elegantly derive the transition probability of field fluctuations, the uncertainty relation, and the Schrödinger equation of the wave functional. Furthermore, by defining the information metrics for field fluctuations using general definitions of relative entropy, we obtain a generalized Schrödinger equation of the wave functional that depends on the order of relative entropy. Our results demonstrate that the extended least action principle can be applied to derive both non-relativistic quantum mechanics and relativistic quantum scalar field theory. We expect it can be further used to obtain quantum theory for non-scalar fields.

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.

Luigi Accardi, Igor Vasil'evich Volovich, Yun Gang Lu

Junho Suh, Alan J Weinstein, Chan U Lei +5 more

Quantum fluctuations of the light field used for continuous position detection produce stochastic back-action forces and ultimately limit the sensitivity. To overcome this limit, the back-action forces can be avoided by giving up complete knowledge of the motion, and these types of measurements are called "back-action evading" or "quantum nondemolition" detection. We present continuous two-tone back-action evading measurements with a superconducting electromechanical device, realizing three long-standing goals: detection of back-action forces due to the quantum noise of a microwave field, reduction of this quantum back-action noise by 8.5 ± 0.4 decibels (dB), and measurement imprecision of a single quadrature of motion 2.4 ± 0.7 dB below the mechanical zero-point fluctuations. Measurements of this type will find utility in ultrasensitive measurements of weak forces and nonclassical states of motion.

Philippe A. Martin, FRANÇOIS ROTHEN