AUTHOR=Marcer Peter , Rowlands Peter 

TITLE=Nilpotent Quantum Mechanics: Analogs and Applications

JOURNAL=Frontiers in Physics

VOLUME=Volume 5 - 2017

YEAR=2017

URL=https://www.frontiersin.org/journals/physics/articles/10.3389/fphy.2017.00028

DOI=10.3389/fphy.2017.00028

ISSN=2296-424X

ABSTRACT=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.