On supersymmetric fermion lattice systems
Hajime Moriya
TL;DR
This paper develops a rigorous mathematical framework for supersymmetric fermion lattice systems, constructing supersymmetric dynamics without Grassmann numbers and analyzing properties of superderivations.
Contribution
It introduces a novel C*-algebraic approach to supersymmetric fermion systems, avoiding Grassmann variables and establishing criteria for supersymmetric dynamics.
Findings
Constructed supersymmetric C*-dynamics using superderivations
Established properties of superderivations on fermion lattices
Provided criteria for superderivations to generate supersymmetric dynamics
Abstract
We provide a mathematically rigorous framework for supersymmetric fermion lattice systems. We construct supersymmetric C*-dynamics in terms of a nilpotent superderivation and a one-parameter group of automorphisms on the CAR-algebra. (We do not make use of Grassmann numbers.) We establish several basic properties of superderivations on the fermion lattice system. Among others, we obtain a criterion of superderivations to yield supersymmetic dynamics.
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Taxonomy
TopicsQuantum Mechanics and Non-Hermitian Physics · Algebraic structures and combinatorial models · Quantum chaos and dynamical systems