 Klein-Gordon inner product

ID: klein-gordon-inner-product

Codex  0 Created 2026-09-24 Updated 2026-09-24

For complex solutions of the Klein-Gordon equation,

(ϕ_{1}, ϕ_{2})_{K G} = i \int_{Σ} d Σ^{a} (ϕ_{1}^{*} \nabla_{a} ϕ_{2} - ϕ_{2} \nabla_{a} ϕ_{1}^{*}) .

The associated current is conserved, so the inner product is independent of the Cauchy hypersurface when boundary flux vanishes.

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