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Richard Gill

Jun 17, 2022, 1:57:15 PM6/17/22
to Bell inequalities and quantum foundations, Richard Gill, Richard Gill

This is a test. I'm putting these equations in slides I'm writing for a conference in London in a week and a half,

- \cos(\delta) ~ ~ = -\frac12 \bigl( e^{i\delta} + e^{-i\delta}\bigr)

= ~ -\int\limits_{\omega \in  \Omega} \,\int\limits_{\theta \in  [0, 2 \pi)}\sum\limits_n c_n(\omega) e^{i n \theta} \sum\limits_{n'} c_{n'} (\omega)e^{i n' (\theta +\delta)} \,\frac{\textrm d \theta}{2 \pi} \,\mathbb P(\textrm d\omega)

 =~ -\int\limits_{\omega \in  \Omega} \,\int\limits_{\theta \in  [0, 2 \pi)}\sum\limits_{n, n'} c_n(\omega)  c_{n'}(\omega) e^{i (n + n')\theta} e^{i n' \delta}\, \frac{\textrm d \theta}{2 \pi} \, \mathbb P(\textrm d\omega)

 =~ -\int\limits_{\omega \in  \Omega}\sum\limits_{n} c_n(\omega)  c_{-n}(\omega)  e^{i n \delta} \,\mathbb P(\textrm d\omega)

 =~ - \sum\limits_{n} \mathbb E |c_n(\omega)|^2  e^{i n \delta}

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