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Examples of antiunitary operator other than time reversal operator

Physics Asked by Leo L. on October 1, 2021

It is well-known that time reversal operation is implemented as an anti-unitary operator. I wonder what are some other examples of anti-unitary operators that appear in the context of quantum mechanics, or physics in general.

One Answer

Just for future reference, an example I encountered recently is the following: in the Bogoliubov-de Gennes (BdG) theory of superconductivity, the Hamiltonian has particle-hole symmetry. And the corresponding transformation is also implemented as an anti-unitary operator, as the following: $$ begin{pmatrix} 0 &boldsymbol{1} boldsymbol{1} & 0 end{pmatrix} K $$ where $K$ is the complex conjugation operator, and $boldsymbol{1}$ has a dimension of $(text{number of bands})cdot 2$ . There could be an additional factor of 2 if including spin degeneracy.

It would be great to hear others' input on other examples of anti-unitary operator in physics.

Answered by Leo L. on October 1, 2021

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