Trace class properties of resolvents of Callias operators (Q6062692)

Let \(H^r\) be the tensorial product of \(\mathbb C^r\) by \(H\), a separable complex Hilbert space. and \(A=(A(x))_{x\in \mathbb R^d}\) be a family of self-adjoint operator on \(H^r\). Let \(c\nabla\) be the Dirac operator on \(\mathbb R^d\) and \(D:=ic\nabla+A(X)\). The author provides conditions on \(A\) such that the resolvent powers of \((D^*D+1)^{-N}-(DD^*+1)^{-N}\) belongs to the one-Schatten-von Neumann operator on the Hilbert space \(L_2(\mathbb R^d,H^r)\) for \(N\in\mathbb N\).