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Haifeng Yang edited Quantizing K G equation.tex
over 10 years ago
Commit id: 414a470555b1e76e7388eae2ffc86f3c6fd3cfce
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$$[\hat{\pi}(\mathbf{x}), \hat{\phi}(\mathbf{y})] = - i \hbar \delta^{(3)} (\mathbf{x} - \mathbf{y})$$
Example: For $\mathcal{L} = \frac{1}{2}\dot{\phi}^2 - \frac{1}{2}(\nabla \phi)^2 - \frac{1}{2}m^2 \phi^2$:
$$\mathcal{H} = \frac{1}{2} \pi^2 + \frac{1}{2} (\nabla
\phi)$^2 \phi)^2 + \frac{1}{2} m^2 \phi^2$$
Note: this is not Lorentz inv.
\end{enumerate}