From 1d87db1b84444d090017e261e5ecbdc2d96c95e3 Mon Sep 17 00:00:00 2001 From: Riccardo Finotello Date: Thu, 3 Dec 2020 14:39:18 +0100 Subject: [PATCH] Typos Signed-off-by: Riccardo Finotello --- sec/part2/divergences.tex | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/sec/part2/divergences.tex b/sec/part2/divergences.tex index a023e13..d1d5e97 100644 --- a/sec/part2/divergences.tex +++ b/sec/part2/divergences.tex @@ -21,7 +21,7 @@ The issue can be roughly traced back to the vanishing volume of a subspace and t As an introduction to the problem we first deal with singularities of the open string sector. We try to build a consistent scalar \qed and show that the vertex with four scalar fields is ill defined. -Divergences in scalar QED are due to the behaviour of the eigenfunctions of the scalar d'Alembertian near the singularity but in a somehow unexpected way. +Divergences in scalar \qed are due to the behaviour of the eigenfunctions of the scalar d'Alembertian near the singularity but in a somehow unexpected way. Near the singularity $u = 0$ in lightcone coordinates almost all eigenfunctions behave as $\frac{1}{\sqrt{\abs{u}}} e^{i \frac{\cA}{u}}$ with $\cA \neq 0$. The product of $N$ eigenfunctions gives a singularity $\abs{u}^{-N/2}$ which is technically not integrable. However the exponential term $e^{i \frac{\cA}{u}}$ allows for an interpretation as distribution when $\cA = 0$ is not an isolated point.