Van der Waerden calculus with commuting spinor variables and the Hilbert-Krein structure of the superspace

Details Van der Waerden calculus with commuting spinor variables and the Hilbert-Krein structure of the superspace Van der Waerden calculus with commuting spinor variables and the Hilbert-Krein structure of the superspace

2004-08-26

arxiv.org/abs/hep-th/0408195v2

Mod.Phys.Lett. A20 (2005) 1239-1250

Physics

High Energy Physics

High Energy Physics - Theory

14 pages

Scientific paper

10.1142/S0217732305017251

Working with anticommuting Weyl(or Mayorana) spinors in the framework of the van der Waerden calculus is standard in supersymmetry. The natural frame for rigorous supersymmetric quantum field theory makes use of operator-valued superdistributions defined on supersymmetric test functions. In turn this makes necessary a van der Waerden calculus in which the Grassmann variables anticommute but the fermionic components are commutative instead of being anticommutative. We work out such a calculus in view of applications to the rigorous conceptual problems of the N=1 supersymmetric quantum field theory.

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