7
votes
2answers
185 views

A problematic integral in calculating the entanglement entropy in 1+1 D free massive bosonic field theory

I encountered a curious integration identity when I was reading the paper by Pasquale Calabrese and John Cardy on the entanglement entropy of 1+1D quantum field theory (arXiv). The identity is given ...
1
vote
1answer
101 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 $ ...
6
votes
1answer
198 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 ...
3
votes
2answers
222 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 ...