Spontaneous symmetry breaking and mass generation as built-in phenomena in logarithmic nonlinear quantum theory

TL;DR

This paper explores how logarithmic nonlinearity in quantum wave equations can inherently cause spontaneous symmetry breaking and mass generation, linking vacuum properties to observable particle masses and topological solutions.

Contribution

It demonstrates that logarithmic nonlinearity can induce symmetry breaking and mass generation without additional mechanisms, providing models for photon mass and discussing topological aspects.

Findings

Photon mass can be expressed via elementary charge and nonlinearity length

Logarithmic nonlinearity leads to spontaneous symmetry breaking

Topological solitonic solutions are possible in the theory

Abstract

Our primary task is to demonstrate that the logarithmic nonlinearity in the quantum wave equation can cause the spontaneous symmetry breaking and mass generation phenomena on its own, at least in principle. To achieve this goal, we view the physical vacuum as a kind of the fundamental Bose-Einstein condensate embedded into the fictitious Euclidean space. The relation of such description to that of the physical (relativistic) observer is established via the fluid/gravity correspondence map, the related issues, such as the induced gravity and scalar field, relativistic postulates, Mach's principle and cosmology, are discussed. For estimate the values of the generated masses of the otherwise massless particles such as the photon, we propose few simple models which take into account small vacuum fluctuations. It turns out that the photon's mass can be naturally expressed in terms of the elementary electrical charge and the extensive length parameter of the nonlinearity. Finally, we outline the topological properties of the logarithmic theory and corresponding solitonic solutions.