In (3.87, pag. 53) Peskin and Schroeder write $$\psi(\vec{x}) = \int\frac{d^{3}p}{(2\pi)^{3}} \frac{1}{\sqrt{2E_{\vec{p}}}} e^{i\vec{p} \cdot \vec{x}} \sum_{s=1,2} (a_{\vec{p}}^{s}u^{s}(\vec{p}) + b_{-\vec{p}}^{s}v^{s}(-\vec{p})) $$ and then compute

$$[\psi(\vec{x}),\psi^{\dagger}(\vec{y})]=\int\frac{d^3p d^3q}{(2\pi)^{6}} \frac{1}{\sqrt{2E_{\vec{p}} 2E_{\vec{q}}}} e^{i(\vec{p} \cdot {\vec{x}}-\vec{q} \cdot {\vec{y}})} \sum_{r,s} ([a_{\vec{p}}^{r},a_{\vec{q}}^{s \dagger}] u^{r}(\vec{p}) \bar{u}^{s}(\vec{q}) + [b_{\vec{p}}^{r},b_{\vec{q}}^{s \dagger}] v^{r}(-\vec{p}) \bar{v}^{s}(-\vec{q})) \gamma^{0}$$

Where does the $ \gamma^{0} $ at the end come from?

In (3.87, page. 53) Peskin and Schroeder write $$\psi(\vec{x}) = \int\frac{d^{3}p}{(2\pi)^{3}} \frac{1}{\sqrt{2E_{\vec{p}}}} e^{i\vec{p} \cdot \vec{x}} \sum_{s=1,2} (a_{\vec{p}}^{s}u^{s}(\vec{p}) + b_{-\vec{p}}^{s}v^{s}(-\vec{p})) $$ and then compute

$$[\psi(\vec{x}),\psi^{\dagger}(\vec{y})]=\int\frac{d^3p d^3q}{(2\pi)^{6}} \frac{1}{\sqrt{2E_{\vec{p}} 2E_{\vec{q}}}} e^{i(\vec{p} \cdot {\vec{x}}-\vec{q} \cdot {\vec{y}})} \sum_{r,s} ([a_{\vec{p}}^{r},a_{\vec{q}}^{s \dagger}] u^{r}(\vec{p}) \bar{u}^{s}(\vec{q}) + [b_{\vec{p}}^{r},b_{\vec{q}}^{s \dagger}] v^{r}(-\vec{p}) \bar{v}^{s}(-\vec{q})) \gamma^{0}$$

Where does the $ \gamma^{0} $ at the end come from?

In (3.87) Peskin and Schroeder write $$\psi(\vec{x}) = \int\frac{d^{3}p}{(2\pi)^{3}} \frac{1}{\sqrt{2E_{\vec{p}}}} e^{i\vec{p} \cdot \vec{x}} \sum_{s=1,2} (a_{\vec{p}}^{s}u^{s}(\vec{p}) + b_{-\vec{p}}^{s}u^{s}(-\vec{p})) $$ and then compute

$$[\psi(\vec{x}),\psi^{\dagger}(\vec{y})]=\int\frac{d^3p d^3q}{(2\pi)^{6}} \frac{1}{\sqrt{2E_{\vec{p}} 2E_{\vec{q}}}} e^{i(\vec{p} \cdot {\vec{x}}-\vec{q} \cdot {\vec{y}})} \sum_{r,s} ([a_{\vec{p}}^{r},a_{\vec{q}}^{s \dagger}] u^{r}(\vec{p}) \bar{u}^{s}(\vec{q}) + [b_{\vec{p}}^{r},b_{\vec{q}}^{s \dagger}] v^{r}(-\vec{p}) \bar{v}^{s}(-\vec{q})) \gamma^{0}$$

Where does the $ \gamma^{0} $ at the end come from?

In (3.87, pag. 53) Peskin and Schroeder write $$\psi(\vec{x}) = \int\frac{d^{3}p}{(2\pi)^{3}} \frac{1}{\sqrt{2E_{\vec{p}}}} e^{i\vec{p} \cdot \vec{x}} \sum_{s=1,2} (a_{\vec{p}}^{s}u^{s}(\vec{p}) + b_{-\vec{p}}^{s}v^{s}(-\vec{p})) $$ and then compute

$$[\psi(\vec{x}),\psi^{\dagger}(\vec{y})]=\int\frac{d^3p d^3q}{(2\pi)^{6}} \frac{1}{\sqrt{2E_{\vec{p}} 2E_{\vec{q}}}} e^{i(\vec{p} \cdot {\vec{x}}-\vec{q} \cdot {\vec{y}})} \sum_{r,s} ([a_{\vec{p}}^{r},a_{\vec{q}}^{s \dagger}] u^{r}(\vec{p}) \bar{u}^{s}(\vec{q}) + [b_{\vec{p}}^{r},b_{\vec{q}}^{s \dagger}] v^{r}(-\vec{p}) \bar{v}^{s}(-\vec{q})) \gamma^{0}$$

Where does the $ \gamma^{0} $ at the end come from?