A glimpse on the role of Grassmann Algebra in Trace Dynamics

Thursday, February 18, 2016
Euler lecture Hall
Stefano Bacchi (PhD student, University of Trieste)
In the formulation of an underlying theory for Quantum Mechanics, Adler builds Trace Dynamics by using traces of matrices with entries which are combinations of Grassmann variables. These combinations are a subset of the Grassmann algebra. Given a brief outline of the main pillars of Trace Dynamics, a quasi-mathematical approach is tempted in order to clarify the mathematical framework and the role of the Grassmann algebra.
[1] "Quantum Theory as an emergent phenomenon" S.L.Adler (2004); [2] "Phase Space Methods for Degenerate Quantum Gases" Dalton, Jeffers, Barnett (2015); [3] "An Attempt of Construction for the Grassmann Numbers" Bentìn (2006); [4] "Tensor spaces and exterior algebra" Yokonuma; [5] "Quadratic mappings and Clifford algebras" Helmstetter, Micali. [6] "Grassmann Numbers and Clifford-Jordan-Wigner Representation of Supersymmetry" Sultan Catto, Yoon S. Choun, Yasemin Gurcan, Amish Khalfan, Levent Kurt.