A glimpse on the role of Grassmann Algebra in Trace Dynamics

Date:

Thursday, February 18, 2016

Room:

Euler lecture Hall

Speaker:

Stefano Bacchi (PhD student, University of Trieste)

Abstract:

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.

References:

[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.