On the Moyal Star Product of Resurgent Series

Abstract: We analyze the Moyal star product in deformation quantization from the resurgence theory perspective. By putting algebraic conditions on Borel transforms, one can define the space of ``algebro-resurgent series'' (a subspace of $1$-Gevrey formal series in $i\hbar/2$ with coefficients in $C{q,p}$), which we show is stable under Moyal star product.