2014/07/21 by Daniel Bennequin, Bennequin, Daniel, Michel Egeileh +1
Mathematics · Physics and Astronomy · #53B50 #58A50 #81T60 #Advanced Differential Geometry Research #Black Holes and Theoretical Physics #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Waves and Solitons #math-ph #math.MP #msc:53B50 #msc:58A50 #msc:81T60
paper · pdf · doi:10.48550/arxiv.1407.5506
40 pages
arxiv created 2014/07/21 · openalex publication_date 2014/07/21 · arxiv updated 2014/07/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
It is known that every irreducible unitary representation of positive energy of the Poincaré group can be realized as a subspace of tensor fields on Minkowski spacetime subjected to suitable partial differential equations. We first describe geometrically the general mechanism that produces, via Fourier transform, the invariant differential operators corresponding to those representations. Then, using a super-version of the Fourier transform, we show explicitly how a massive irreducible unitary representation of the super Poincaré group in dimension (4|4) can be realized as a linear sub-supermanifold of suitably constrained superfunctions. In this way, we obtain supersymmetric equations in terms of ordinary (non-Grassmannian) fields. Finally, using the functor of points, we show how our equations can be related in a natural way to the Wess-Zumino equations for massive chiral superfields.