The ground state wave functional for the photon theory is given as(adsbygoogle = window.adsbygoogle || []).push({});

[tex] \Psi_0[\tilde{a}] = \eta \exp \left(-\frac{1}{2} \int \frac{d^3k}{(2\pi)^3} \frac{(\vec{k}\times\tilde{a}(\vec{k}))\cdot(\vec{k}\times\tilde{a}(-\vec{k}))}{|\vec{k}|}\right)[/tex](10.81)

where [tex]\tilde{a}[/tex] is given as the Fourier transform of [tex]a[/tex], that is,

[tex] a_i(\vec{x}) = \int \frac{d^3k}{(2\pi)^3}\tilde{a}_i(\vec{k})e^{i\vec{k}\cdot\vec{x}} [/tex](10.67)

Transforming back to [tex]a[/tex], the book now says that (10.81) is equivalent to

[tex] \Psi_0[a] = \eta \exp \left(-\frac{1}{(2\pi)^2} \int d^3x d^3y \frac{(\nabla\times\vec{a}(\vec{x}))\cdot(\nabla\times\vec{a}(\vec{y}))}{|\vec{x}-\vec{y}|^2}\right) [/tex](10.83)

I've had to think about this for a long time, and I'm still not sure I understand it exactly.

**Physics Forums - The Fusion of Science and Community**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Fourier transorm problem has me stumped

Loading...

Similar Threads for Fourier transorm problem | Date |
---|---|

I Measurement problems? | Yesterday at 1:51 PM |

I Normalization and the probability amplitude | Apr 2, 2018 |

I Negative and Positive energy modes of KG equation | Dec 18, 2017 |

I Fourier conjugates and momentum | Oct 3, 2017 |

I 'Normalisation' of Fourier Transforms in QFT | Aug 1, 2017 |

**Physics Forums - The Fusion of Science and Community**