Nilpotent Quantum Mechanics: Analogs and Applications

Frontiers in Physics

Marcer, Peter¹  Rowlands, Peter² 

[1] Independent Researcher, St. Raphael, France;Oliver Lodge Laboratory, Department of Physics, University of Liverpool, Liverpool, United Kingdom

关键词: universal rewrite system;    self-organization;    nilpotent quantum mechanics;    Renormalization Group;    Visual Cortex Organization;   

DOI  :  10.3389/fphy.2017.00028

学科分类：物理（综合）

来源: Frontiers

【 摘 要 】

The most significant characteristic of nilpotent quantum mechanics is that the quantum system (fermion state) and its environment (vacuum) are, in mathematical terms, mirror images of each other. So a change in one automatically leads to corresponding changes in the other. We have used this characteristic as a model for self-organization, which has applications well beyond quantum physics. The nilpotent structure has also been identified as being constructed from two commutative vector spaces. This construction has a number of identifiable characteristics which we can expect to find in systems where self-organization is dominant, and a case presented after the publication of a paper by us on ‘The ‘Logic’ of Self-Organizing Systems’,1 in the organization of the neurons in the visual cortex. We expect to find many more complex systems where our general principles, based, by analogy, on nilpotent quantum mechanics, will apply.

【 授权许可】

CC BY