Section on renormalization updated.

pages/Renormalization.tex

@@ -31,10 +31,10 @@ \subsection{Renormalization constants and mass
 generic masses, coupling constants and fields we can write
 
 \begin{align*}
-g_{\textrm{bare}} &=  \mu^{n \varepsilon} Z_g g_{\textrm{ren}} \\
-m_{\textrm{bare}} &=  Z_m m_{\textrm{ren}} \\
-\psi_{\textrm{bare}} &=  \sqrt{Z_m} \psi_{\textrm{ren}} \\
-A^\mu_{\textrm{bare}} &=  \sqrt{Z_A} A^\mu_{\textrm{ren}} \\
+g_{\textrm{bare}} &=  \mu^{n \varepsilon} Z_g g_{\textrm{ren}}, \\
+m_{\textrm{bare}} &=  Z_m m_{\textrm{ren}}, \\
+\psi_{\textrm{bare}} &=  \sqrt{Z_m} \psi_{\textrm{ren}}, \\
+A^\mu_{\textrm{bare}} &=  \sqrt{Z_A} A^\mu_{\textrm{ren}}. \\
 \end{align*}
 
 The renormalization scale \(\mu\) is needed to account for the fact,
@@ -93,8 +93,8 @@ \subsection{Renormalization constants and mass
 
 where \(\delta Z_x\) contains poles in \(\varepsilon\) and possibly also
 finite pieces (depending on the chosen renormalization scheme).
-Parametrically, \(Z_x\) is of order of the small coupling constant so
-that we can ``expand'' in it as if \(Z_x \ll 1\).
+Parametrically, \(\delta Z_x\) is of order of the small coupling
+constant so that we can ``expand'' in it as if \(\delta Z_x \ll 1\).
 
 \hypertarget{examples-of-renormalized-and-counter-term-lagrangians}{%
 \subsection{Examples of renormalized and counter-term
@@ -175,8 +175,8 @@ \subsection{Feynman rules}\label{feynman-rules}}
 
 Although those can be always derived by hand, doing so automatically is
 more convenient and allows to avoid many stupid mistakes. To this aim it
-useful to employ \href{https://feynrules.irmp.ucl.ac.be/}{FeynRules} for
-generating the corresponding FeynArts model. When writing down the
+is useful to employ \href{https://feynrules.irmp.ucl.ac.be/}{FeynRules}
+for generating the corresponding FeynArts model. When writing down the
 Lagrangian of our model we need to multiply every term in the counter
 term Lagragnian by \texttt{FR\$CT}, for example