%A Marcer,Peter
%A Rowlands,Peter
%D 2017
%J Frontiers in Physics
%C
%F
%G English
%K universal rewrite system,self-organization,nilpotent quantum mechanics,Renormalization Group,Visual Cortex Organization
%Q
%R 10.3389/fphy.2017.00028
%W
%L
%M
%P
%7
%8 2017-July-18
%9 Original Research
%+ Peter Rowlands,Oliver Lodge Laboratory, Department of Physics, University of Liverpool,Liverpool, United Kingdom,p.rowlands@liverpool.ac.uk
%#
%! Nilpotent Quantum Mechanics: Analogues and Applications
%*
%<
%T Nilpotent Quantum Mechanics: Analogs and Applications
%U https://www.frontiersin.org/article/10.3389/fphy.2017.00028
%V 5
%0 JOURNAL ARTICLE
%@ 2296-424X
%X 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.