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- Starting from the Lagrangian for a complex scalar field obtain the Hamiltonian for a free complex Klein Gordon field.
- Write ETCR and for the quantized field prove that \begin{equation}\label{EQ01} \big[H, \pi(x)\big] = - i \big( \nabla^2- \mu^2\big) \phi^*(x) . \end{equation}
- Does relation,\eqRef{EQ01}, hold only as equal time commutator or for \(H\) and \(\pi(x)\) at arbitrary different times ? Explain your answer.
- Use \EqRef{EQ01} to derive the usual Euler Lagrange equation of motion for the complex scalar field.
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