Outline and abstract

Signed-off-by: Riccardo Finotello <riccardo.finotello@gmail.com>

sec/part1/introduction.tex

@@ -28,7 +28,7 @@ Such surface can have different topologies according to the nature of the object
 
 As the action of a point particle is proportional to the length of its trajectory (its \emph{worldline}), the same object for a string is proportional to the area of the worldsheet in the original formulation by Nambu and Goto.
 The solutions of the classical equations of motion (\eom) are therefore strings spanning a worldsheet of extremal area.
-While Nambu and Goto's formulation is fairly direct in its definition, it usually best to work with Polyakov's action~\cite{Polyakov:1981:QuantumGeometryBosonic}
+While Nambu and Goto's formulation is fairly direct in its definition, it usually best to work with Polyakov's action~\cite{Polyakov:1981:QuantumGeometryBosonic}:
 \begin{equation}
   S_P[ \gamma, X ]
   =
@@ -42,7 +42,7 @@ While Nambu and Goto's formulation is fairly direct in its definition, it usuall
   \eta_{\mu\nu}.
   \label{eq:conf:polyakov}
 \end{equation}
-The \eom for the string $X^{\mu}(\tau, \sigma)$ is therefore
+The \eom for the string $X^{\mu}(\tau, \sigma)$ is therefore:
 \begin{equation}
   \frac{1}{\sqrt{- \det \gamma}}\,
   \ipd{\alpha}