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$\newcommand{\matrixelement}[3]{\langle#1|#2|#3\rangle}\newcommand{\dd}[2][]{\frac{d#1}{d#2}}$
For a self coupled scalar theory with interaction Lagrangian density given by
\begin{equation} \mathscr {L}_{\text{int}}= \frac{\lambda}{3!}\phi(x)^3 \end{equation}
Compute and write your answers as integrals of expressions involving propagator in position space.
\begin{eqnarray} (a)&& \int d^4y_1\int d^4y_2\int d^4y_3 \matrixelement{0}{T(\phi(x_1)\phi(x_2) \mathscr{ L}(y_1) \mathscr {L}(y_2)\mathscr {L}(y_3)}{0} \\ (b) && \int d^4y_1 \int d^4y_2\matrixelement{0}{T(\phi(x_1)\phi(x_2)
\mathscr{L}(y_1) \mathscr{L}(y_2)}{0}. \end{eqnarray}
Draw position space Feynman diagram in each case.
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\begin{equation} \mathscr L_{
\begin{equation} \mathscr L_{\text{int}}= \frac{\lambda}{3!}phi(x)^3:\end{equation} Compute \begin{eqnarray} (a) && \int d^4y_1 \int d^4y_2\matrixelement{0}{T(\phi(x_1)\phi(x_2) $\mathscr L$(y_1) $\mathscr L$(y_2){0}\\ (b) && \end{eqnarray}