Timeline for Dimensional regularization of a divergent integral
Current License: CC BY-SA 4.0
3 events
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| Oct 28, 2019 at 18:13 | comment | added | Seth Whitsitt | That's true - one should also ask that the integrals are holomorphic functions of $d$ with $\alpha$ fixed (and vice-versa), so that divergences take form of poles which may be subtracted. Given that the integral is zero for all $d \neq 2 \alpha$, the only value you can assign to it at $d = 2 \alpha$ consistent with this requirement is also zero. | |
| Oct 28, 2019 at 15:09 | comment | added | MadMax | "the first two properties immediately imply the "identity" $\int \frac{d^d p}{(2 \pi)^d} \frac{1}{(p + q)^{2\alpha}} = 0$ for all $d$ and $\alpha$" : not true for $d=2\alpha$, i.e. logarithmically divergent case. | |
| Oct 27, 2019 at 22:04 | history | answered | Seth Whitsitt | CC BY-SA 4.0 |