The integral:(adsbygoogle = window.adsbygoogle || []).push({});

[itex]\int[/itex]d[itex]^{3}k[/itex][itex]\frac{1}{k^{2}+m^{2}}[/itex]

is linearly divergent i.e. ultraviolet divergent.

However, If one performs dimensional regularization to the above integral:

[itex]\frac{1}{(2\pi)^d}[/itex][itex]\int[/itex]d[itex]^{d}k[/itex][itex]\frac{1}{k^{2}+m^{2}}[/itex]=[itex]\frac{(m^{2})^{d/2-1}}{(4\pi)^{d/2}}[/itex][itex]\Gamma(1-d/2)[/itex]

As you can notice that the poles of the Gamma function are for even dimension i.e. d=2,4,6..etc and that the integral is convergent for d=3 for example!!!

What is the reason behind this convergence? Is it due to the Veltman's formula:

[itex]\frac{1}{(2\pi)^d}[/itex][itex]\int[/itex]d[itex]^{d}k[/itex][itex] (k^{2})^{n-1}[/itex] = 0, for n=0,1,2,..

I am dealing with a divergent integral of power divergence (ultraviolet, quadratic, quartic,... and no logarithmic divergence). Do you advise me to use dimensional regularization or other methods?

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Ultraviolet via dimensional regularization

Can you offer guidance or do you also need help?

Draft saved
Draft deleted

**Physics Forums | Science Articles, Homework Help, Discussion**