Chiral Symmetry Operator

[thatboi]

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?

 

[DrDu]

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.