Complex structure on the Klein-Gordon solution space
ID: complex-structure-on-the-klein-gordon-solution-space
On the real Klein-Gordon field solution space with conserved symplectic form , a compatible real-linear map obeys , preserves , and makes positive definite. Its eigenspace in the complexified space has positive Klein-Gordon inner product with the convention . It defines the one-particle Hilbert space and a free-field Fock vacuum.
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