Nilpotent Quantum Mechanics: Analogs and Applications

• Main Authors: Peter Marcer, Peter Rowlands
• Format: Article
• Language: English
• Published: Frontiers Media S.A. 2017-07-01
• Series: Frontiers in Physics
• Subjects: universal rewrite system; self-organization; nilpotent quantum mechanics; renormalization group
• Online Access: http://journal.frontiersin.org/article/10.3389/fphy.2017.00028/full

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.