Application of non-standard analysis to the quantum theory of particles and fields

Anonymous

The particle concept is widely used in quantum field theory, yet its applicability is often assumed rather than structurally defined. This paper introduces explicit criteria for particlehood based on identifiability, persistence, and transportability, and applies them within the framework of the Standard Model. It is shown that field quantization alone does not imply the existence of particles, and that several degrees of freedom commonly treated as particles fail to meet these criteria. In particular, gluons and virtual excitations are identified as non-particles in a principled sense, while photons occupy a boundary regime in which particle language is only conditionally valid. The analysis leaves the formalism, symmetries, and predictive success of the Standard Model entirely intact, while clarifying the interpretational limits of particle-based descriptions. By separating computational structures from ontological commitments, the work provides a disciplined reorganization of particle language that resolves longstanding conceptual ambiguities in quantum field theory.

H. Muirhead

Stefano Gogioso, Fabrizio Genovese

In this work, we use tools from non-standard analysis to introduce infinite-dimensional quantum systems and quantum fields within the framework of Categorical Quantum Mechanics. We define a dagger compact category *Hilb suitable for the algebraic manipulation of unbounded operators, Dirac deltas and plane-waves. We cover in detail the construction of quantum systems for particles in boxes with periodic boundary conditions, particles on cubic lattices, and particles in real space. Not quite satisfied with this, we show how certain non-separable Hilbert spaces can also be modelled in our non-standard framework, and we explicitly treat the cases of quantum fields on cubic lattices and quantum fields in real space.

Peter Bongaarts

Jincheng Zhang

This paper presents a novel approach to quantum field theory, specifically tailored for the analysis of particle decay, leveraging non-Euclidean geometry to model the collapse of particles. The core of this research focuses on the concept of geometric collapse, where the underlying structure of a particle's quantum state is determined by a non-Euclidean geometry. We propose a theoretical framework that incorporates geometric properties, aiming to reveal unexpected features and potential deviations from standard quantum mechanics. This work represents a significant departure from existing models, offering a fundamentally different perspective on the dynamics of decay and potentially unlocking new insights into the fundamental laws of the universe. The investigation will explore the implications of such a theory on the observed behavior of quantum particles during decay processes, investigating how geometric properties influence the collapse process.

Vladimir Anashin