2004/10/31 by Vahagn Nazaryan, Carl E. Carlson
Mathematics · Physics and Astronomy · #Advanced Operator Algebra Research #Black Holes and Theoretical Physics #D-term #F-term #Lorentz transformation #Mathematical physics #Mathematics #Minkowski space #Noncommutative and Quantum Gravity Theories #Noncommutative geometry #Physics #Pure mathematics #Quantum mechanics #Spinor #Star product #Superspace #Supersymmetry #hep-th
paper · pdf · doi:10.1103/physrevd.71.025019
published as Phys.Rev. D71 (2005) 025019 · 8 pages, added references, two-column format, published in PRD
openalex publication_date 2005/01/26 · arxiv created 2005/01/27 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
There is much discussion of scenarios where the space-time coordinates x^\ensuremathμ are noncommutative. The discussion has been extended to include nontrivial anticommutation relations among spinor coordinates in superspace. A number of authors have studied field theoretical consequences of the deformation of N=1 superspace arising from nonanticommutativity of coordinates \ensuremathθ, while leaving \ensuremathθ's anticommuting. This is possible in Euclidean superspace only. In this note we present a way to extend the discussion by making both \ensuremathθ and \ensuremathθ coordinates nonanticommuting in Minkowski superspace. We present a consistent algebra for the supercoordinates, find a star-product, and give the Wess-Zumino Lagrangian LWZ within our model. It has two extra terms due to non(anti)commutativity. The Lagrangian in Minkowski superspace is always manifestly Hermitian and for LWZ it preserves Lorentz invariance.