Why is K an anti-unitary operator in (26)?

In summary, the question asks if the equation (U_T * K) * (U_C * K) = U_T * U_C^* is true because K is a unitary operator and (K * U_C * K) = U_C^* as expected for a unitary transformation. However, it is clarified that K is actually an anti-unitary operator that implements complex conjugation.
  • #1
thatboi
121
18
Hey all,
I just wanted to double check my understanding of (26) in the following notes: https://arxiv.org/pdf/1512.08882.pdf.
Is the reason that ##(U_{T}\cdot K) \cdot (U_{C}\cdot K) = U_{T}\cdot U_{C}^{*}## because ##K## is a unitary operators and thus ##(K\cdot U_{C}\cdot K) = U_{C}^{*}## as we would expect of a unitary transformation?
 
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  • #2
thatboi said:
Hey all,
I just wanted to double check my understanding of (26) in the following notes: https://arxiv.org/pdf/1512.08882.pdf.
Is the reason that ##(U_{T}\cdot K) \cdot (U_{C}\cdot K) = U_{T}\cdot U_{C}^{*}## because ##K## is a unitary operators and thus ##(K\cdot U_{C}\cdot K) = U_{C}^{*}## as we would expect of a unitary transformation?
No, it says explicitly that K is an anti-unitary operator, not a unitary one. Specifically, K implements complex conjugation.
 

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