Journal of Physical Studies 11(2), 142–147 (2007) DOI: https://doi.org/10.30970/jps.11.142 NILPOTENT ELEMENTS IN PHYSICS A. M. Frydryszak Institute of Theoretical Physics, University of Wroclaw, pl. M. Borna 9, 50–204 Wroclaw, Poland

We briefly review some issues of the nilpotent objects in theoretical physics using simple models as an illustration. Nilpotent elements appear at quantum and classical level in several ways. On the one hand there are celebrated BRST operators, external derivative and related with them cohomology theory, on the other hand there are dual numbers which are a less known structure than complex numbers but important in many approaches, then there are commuting nilpotent variables, somehow generalizing the nilpotent but anticommuting Grassmann variables used in super-mathematics and SUSY models. As an interesting fact we note that nilpotent variables demand the use of the generalized light-cone geometry with the metric of the null signature.

PACS number(s): 11.30.Pb, 45.20.Jj

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