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I've read a lot of posts about how Weinberg describes the S-matrix invariance in his book, but none of theme answered my questions.

At page 116, sec 3.3 - "Lorentz Invariance" of Quantum theory of fields vol.1 Weinberg says:

"Since the operator [itex]U(\Lambda, a)[/itex] is unitary we may write

[tex]

S_{\beta\,\alpha}=\langle\Psi_{\beta}^-\mid\Psi_{\alpha}^+\rangle

=\langle\Psi_{\beta}^- \mid U^{\dagger}U\mid \Psi_{\alpha}^+\rangle

[/tex]

From this equation he gets some conditions that the S-matrix has to fulfill.

But if the operator [itex]U(\Lambda, a)[/itex] is unitary, then shouldn't be

[itex]U^{\dagger}U=1[/itex]?

And so the equation above is always satisfied no matter the form of the S matrix!

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# S-matrix in Weinberg book

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