I am working my way through Peskin and Schroeder section 2.2 and trying to show that $T^{00}$ is equivalent to the expression $\frac{1}{2}\pi^2-\frac{1}{2}(\nabla \phi)^2-\frac{1}{2}m^2\phi^2$ in equation (2.8) as it suggests.
From $T^\mu_{\;\;\nu} = \frac{\partial \mathcal{L}}{\partial (\partial_\mu \phi)}\partial_\nu - \mathcal{L}\delta^\mu_{\;\nu}$, I get:
$\begin{equation} T^\mu_{\;\;\nu} = \frac{1}{2}\partial^\mu\phi\partial_\nu\phi - \mathcal{L}\delta^\mu_{\;\nu} \end{equation}$
and from there:
$\begin{equation} T^{00} = T^0_{\;\;0} = \frac{1}{2}\partial^0\phi\partial_0\phi - \mathcal{L}\delta^0_{\;0} \end{equation} = \frac{1}{2}\dot{\phi}^2 - \frac{1}{2}[\partial_0\phi^2-\partial_1\phi^2-\partial_2\phi^2-\partial_3\phi^2] + \frac{1}{2}m^2\phi^2$
It looks like I have an extra $-\frac{1}{2}\dot\phi^2$ in my result. Did I make a mistake somewhere?