# Quick question on formula

1. Jun 2, 2007

### shoehorn

Suppose that I have an expression of the following form:

$$g_{ik}(x)\pi^{kp}(x') \left( \frac{\partial}{\partial x^p}\frac{\partial}{\partial x'^j} - \frac{\partial}{\partial x^j}\frac{\partial}{\partial x'^p}\right) \delta(x,x')$$

where $g_{ij}$ and $\pi^{ij}(x)$ are tensors and their position-dependence is indicated in the brackets, and $\delta(x,x')$ is the three-dimensional Dirac distribution on a given manifold. My question is, does the above expression vanish identically?