[QUE/QFT-15007] QFT-PROBLEM

Write Klein Gordon equation and the corresponding Lagrangian for a spin zero charged particle in presence an external electromagnetic field. Obtain the Hamiltonian. To the lowest order in \(e\), compute the scattering cross section for Coulomb scattering of a charged pion taking the vector potential to be that of a nucleus of charge density \(\rho(\vec{x})\). Write your answer for cross section in terms in of Fourier transform of \(\rho(\vec{x})\).