Tagged Questions
1
vote
1answer
72 views
the meaning of epsilon in this operator $ \epsilon $
Consider the dimensional regularized integral
$$ \int d^{d}k (k^{2}-m^{2}+i\epsilon)^{-\lambda} $$
For positive $ \lambda $ this integral has a pole at $ k=m $. Is this the reason we we insert the $ ...
3
votes
0answers
117 views
Zeta regularization gone bad
This may sound as a mathematical question, but it should be very familiar to physicists. I am trying to perform an expansion of the function $$f(x) = \sum_{n=1}^{\infty} \frac{K_2(nx)}{n^2 x^2},$$ for ...
2
votes
2answers
149 views
Gaussian type integral with negative power of variable in integrand
How can we compute the integral $\int_{-\infty}^\infty t^n e^{-t^2/2} dt$ when $n=-1$ or $-2$? It is a problem (1.11) in Prof James Nearing's course Mathematical Tools for Physics. Can a situation ...
