\(\newcommand{\ket}[1]{|#1\rangle} \newcommand{\matrixelement}[3]{\langle#1|#2|#3\rangle}\)
For a real free Klein Gordon field, mass \(m\), compute \[ \matrixelement{0}{\phi(x)\phi(y)}{\vec{k}, \vec{q}}\] and show that the result is properly symmetrized wave function for two identical bosons with momenta \(\vec{q},\vec{p}\). Here \(\ket{\vec{k}, \vec{q}}\) is the state with two bosons with momenta \(\vec{k}, \vec{q}\)
$\newcommand{\matrixelement}[3]{\langle#1|#2|#3\rangle}\newcommand{\dd}[2][]{\frac{d#1}{d#2}}${}$\newcommand{\pp}[2][]{\frac{\partial #1}{\partial #2}}${}$\newcommand{\ket}[1]{|#1\rangle}$ {} $\newcommand{\bra}[1]{\langle #1|}$For a real free Klein Gordon field, mass \(m\), compute \[ \matrixelement{0}{\phi(x)\phi(y)}{\vec{k}, \vec{q}}\] and show that the result is properly symmetrized wave function for two identical bosons with momenta \(\vec{q},\vec{p}\). Here \(\ket{\vec{k}, \vec{q}}\) is the state with two bosons with momenta \(\vec{k}, \vec{q}\)
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