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[QUE/QFT-01001] QFT-PROBLEM

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  • Write the Lagrangian for free Schrodinger field and obtain an expression for the Hamiltonian.
  • Using the Poisson bracket form of equations of motion show that the Galilean boost \[\vec{G}[\psi]=\int d^3 x\, \psi^\dagger (m\,\vec{x}+ it \hbar \nabla)\psi,\] is a conserved quantity. How do you interpret this conservation law?

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