So I'm reading Gottfried and Yan's Quantum Mechanics: Fundamentals. On page 284, They state Wigner's Theorem and explain the two cases. One transformation leads to(adsbygoogle = window.adsbygoogle || []).push({}); nocomplex conjugation of the expansion coefficients (unitary) and the other leads to a complex conjugation of the expansion coefficients (antiunitary). Anyway, I'm confused when he states the following.

Applying an antiunitary operator twice results in a unitary operation, since the expansion coefficients are conjugated twice. Therefore the antiunitary operators cannot be represented as a continuous group because for any such operation (call it A) there exists the square root of that operation (A_(1/2)), which when applied twice gives an A and thus any A in the continuous group must be unitary for self-consistency.

The part I don't get:

He then goes on to say "by the same argument, candidates for an antiunitary transformation must be such that A^2 reproduces the original description"

I don't understand why it necessarily has to reproduce the original description. I only understand why it has to be a discrete transformation. Anyone care to shed some light?

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# Wigner's Theorem/Antiunitary Transformation

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