On products of delta distributions and resultants

Michel Bauer (1, 2) , Jean-Bernard Zuber (1, 3)

1 IPHT - Institut de Physique Théorique - UMR CNRS 3681
2 DMA - Département de Mathématiques et Applications - ENS Paris
3 LPTHE - Laboratoire de Physique Théorique et Hautes Energies

We prove an identity in integral geometry, showing that if $P_x$ and $Q_x$ are two polynomials, $\int dx \, \delta(P_x) \otimes \delta(Q_x)$ is proportional to $\delta(R)$ where $R$ is the resultant of $P_x$ and $Q_x$.

Domaines: Physique mathématique [math-ph]

Michel Bauer, Jean-Bernard Zuber. On products of delta distributions and resultants. Symmetry, Integrability and Geometry : Methods and Applications, 2020, 16, pp.083. ⟨10.3842/SIGMA.2020.083⟩. ⟨hal-02869757⟩