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Problem-QFT-05001


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 does it hold 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 Klein Gordon field.

kapoor kapoor's picture 22/10/18

Lectures-EM-12 Maxwell's Equations in Relativistic Notation

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kapoor kapoor's picture 22/10/18

Lectures-EM-12 Potentials as Four Vectors

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kapoor kapoor's picture 22/10/18

Lectures-EM-12 :: Relativistic Transformations of Fields

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kapoor kapoor's picture 22/10/18

EM-12 :: Lecture Notes

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kapoor kapoor's picture 22/10/18

Lectures-QM-33 Non-Relativisic Limit of Position Operators in Quantum Mechanics

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kapoor kapoor's picture 22/10/18

Lectures-QFT-04 Physical Interpretation

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kapoor kapoor's picture 22/10/18

Lectures-QFT-04 Second Quantization of Schrodinger Equation

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kapoor kapoor's picture 22/10/18

Lectures-QFT-01 Hamiltonian Formulation of Classical Fields

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kapoor kapoor's picture 22/10/18

QFT-04 :: Secoond Quantization

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kapoor kapoor's picture 22/10/18

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