New Approaches to Soliton Quantization and Existence for Particle Physics

TL;DR

This paper explores new mathematical methods for analyzing soliton stability, existence without topological charge, and novel quantization approaches, with implications for quantum theory and nuclear physics.

Contribution

It introduces new stability analysis techniques, proposes soliton existence without topological charge, and presents three alternative quantization formalisms with foundational implications.

Findings

Identifies promising systems for energy-minimizing solitons

Develops new second-order stability analysis methods

Proposes three alternative soliton quantization formalisms

Abstract

This paper provides mathematical details related to another new paper which suggests: (1) new approaches to the analysis of soliton stability; (2) families of Lagrangian field theories where solitons might possibly exist even without topological charge; (3) alternative approaches to quantizing solitons, with testable nuclear implications. This paper evaluates the possibility of strong energy-minimizing states in four families of systems, two promising and two not promising. In these examples, it presents new methods for second-order stability analysis, and analyzes persistent multifurcation. Section 6 presents three alternative formalisms for quantizing solitons (topological or nontopological), all of which have major implications for the foundations of quantum theory: (1) the standard formalism, based on functional integration, reinterpreted as an imaginary Markhov Random Field (iMRF) across time and space, with parallels to fuzzy logic; (2) two radically conservative formalisms, consistent with the core of Einstein's vision, based on a true MRF model. Bell's Theorem, bosonization, time-symmetry and macroscopic asymmetry are discussed, along with some testable alternative possibilities and heresies, like nonDoppler redshift.