`Gauging' time reversal symmetry in tensor network states

Understand

It is well known that unitary symmetries can be `gauged', i.e.

• defined to act in a local way, which leads to a corresponding gauge field.
• Gauging, for example, the charge conservation symmetry leads to electromagnetic gauge fields.
• It is an open question whether an analogous process is possible for time reversal which is an anti-unitary symmetry.