deletions | additions       diff --git a/Introduction.tex b/Introduction.tex  index 7099fa5..3c3957d 100644  --- a/Introduction.tex  +++ b/Introduction.tex 
...
\end{equation}  We would invoke quantum field like rules.  Thus we have \begin{equation}  \sum_{k=1}^\infty \sqrt{k}(p_{k} \cdot p_{k+1})\sum_{k'=2}^\infty \sqrt{k'}(p_{k'+1} \cdot p_{k'}) - \sum_{k=2}^\infty \sqrt{k}(p_{k+1} \cdot p_{k})\sum_{k'=1}^\infty \sqrt{k'}(p_{k'} \cdot p_{k'+1}) = I_\infty  \end{equation}  In this representation. But we may also notice that \begin{equation}  \sum_{k=1}^\infty (p_k \cdot p_k) = I_\infty  \end{equation}  And thus the two expressions must be equal!