AUTHOR=Marcer Peter , Rowlands Peter TITLE=Nilpotent Quantum Mechanics: Analogs and Applications JOURNAL=Frontiers in Physics VOLUME=5 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 zero square-root 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.