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Elements of a non-Hermitian quantum theory without Hermitian conjugation - scalar product and scattering

The descripition of in a Hermitian setting seemingly nonlocal and nonperturbative phenomena like confinement or superconductivity is most conveniently performed by generalizing quantum theory to a non-Hermitian regime where these phenomena appear perturbative and local. The short presentation provides a clue how this can be done on the basis of Lorentz covariance while preserving the analyticity of the theory. After deriving with the help of Lorentz covariance a quantum scalar product without making any use of metric or complex conjugation we sketch how the formalism of scattering theory can be extended analytically to a non-Hermitian regime.