- #1
spaghetti3451
- 1,344
- 33
Consider the following integration:
$$\int \frac{d^{4}k}{(2\pi)^{4}}\ \frac{1}{(k^{2}+m^{2})^{\alpha}}=\frac{1}{(4\pi)^{d/2}} \frac{\Gamma\left(\alpha-\frac{d}{2}\right)}{\Gamma(\alpha)}\frac{1}{(m^{2})^{\alpha-d/2}}.$$
---
How does the dependence on ##d## arise in this integral?
Can someone show the intermediate steps in this integration explicitly?
$$\int \frac{d^{4}k}{(2\pi)^{4}}\ \frac{1}{(k^{2}+m^{2})^{\alpha}}=\frac{1}{(4\pi)^{d/2}} \frac{\Gamma\left(\alpha-\frac{d}{2}\right)}{\Gamma(\alpha)}\frac{1}{(m^{2})^{\alpha-d/2}}.$$
---
How does the dependence on ##d## arise in this integral?
Can someone show the intermediate steps in this integration explicitly?