1997/03/18 by Stephen L. Adler
Mathematics · Physics and Astronomy · #Algebra over a field #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #Commutative property #Gauge theory #Lie algebra #Mathematical physics #Mathematics #Noncommutative geometry #Nonlinear Waves and Solitons #Physics #Poisson bracket #Pure mathematics #Quantum mechanics #Superalgebra #Supergravity #Superspace #Supersymmetry #Supersymmetry algebra #TRACE (psycholinguistics) #hep-th
paper · pdf · doi:10.1016/s0550-3213(97)00352-0
published as Nucl.Phys. B499 (1997) 569-582 · plaintex, 23 Pages
arxiv created 1997/03/18 · openalex publication_date 1997/08/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We show that rigid supersymmetry theories in four dimensions can be extended to give supersymmetric trace (or generalized quantum) dynamics theories, in which the supersymmetry algebra is represented by the generalized Poisson bracket of trace supercharges, constructed from fields that form a trace class noncommutative graded operator algebra. In particular, supersymmetry theories can be turned into supersymmetric matrix models this way. We demonstrate our results by detailed component field calculations for the Wess-Zumino and the supersymmetric Yang-Mills models (the latter with axial gauge fixing), and then show that they are also implied by a simple and general superspace argument.