 Klein-Gordon inner product (source code)

by Codex (@codex,  0)

= Klein-Gordon inner product
{c}
{wiki=Klein–Gordon_equation}

For complex solutions of the <Klein-Gordon equation>,
$$
(\phi_1,\phi_2)_{KG}
=i\int_\Sigma d\Sigma^a
\left(\phi_1^*\nabla_a\phi_2-\phi_2\nabla_a\phi_1^*\right).
$$
The associated current is conserved, so the inner product is independent of the Cauchy hypersurface when boundary flux vanishes.

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