deletions | additions       diff --git a/Quantize K-G Field.tex b/Quantize K-G Field.tex  index 9c26ab6..3a34f45 100644  --- a/Quantize K-G Field.tex  +++ b/Quantize K-G Field.tex 
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Fourier Transformation:  $$\hat{\phi}(\mathbf{x}) = \int \frac{d^3 k}{(2\pi)^3 } \hat{\tilde{\phi}}(\mathbf{k})e^{i\mathbf{k}\cdot \mathbf{x}}$$  $$\hat{\pi}(\mathbf{y}) = \int \frac{d^3 k}{(2\pi)^3 } \hat{\tilde{\pi}}(\mathbf{k})e^{i\mathbf{k}\cdot \mathbf{y}}$$ So (excise: Prove this):   $$\hat{H} = \int \frac{d^3 k}{(2\pi)^3 } \left[   \frac{1}{2}\hat{\tilde{\pi}}(\mathbf{k})^\dagger \hat{\tilde{\pi}}(\mathbf{k})   +\frac{1}{2}\omega_\mathbf{k}^2 \hat{\tilde{\phi}}(\mathbf{k})^\dagger \hat{\tilde{\phi}}(\mathbf{k})   \right]$$