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In Peskin & Schroeder QFT book p.59, they said:

The operator $U(\Lambda)$ that implements Lorentz transformations on the states of Hilbert space is unitary, even thought for boosts $\Lambda_{1/2}$ is not unitary.

Why the former $U(\Lambda)$ on the states of Hilbert space is unitary?

Why the not unitary $\Lambda_{1/2}$ would not affect the $U(\Lambda)$ on the states of Hilbert space being unitary or not?

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