Transforming antiunitary symmetries to a normal form

Abstract: We look at explicit ways to bring one or two antiunitary symmetries into a standard form via unitary conjugation. We use the method Wigner introduced to prove that all antiunitary operators are direct sums of small antiunitary rotations. The methods are constructive and can be used to compute the needed unitaries in small examples. When we have two symmetries we can adapt these methods and still get a unitary to conjugate over to where the two symmetries are in a standard form. We cover all eight of the symmetry classes, the ones that involve at least one antiunitary symmetry.