Super Hilbert Space and the Quantum-Mechanical Time Operators

The basic idea of super Hilbert space is to represent physical states by continuous linear functionals on a space of good functions, rather than by functions in a Hilbert space. Since L2 is in one-to-one correspondence with a subset of super Hilbert space, everything that can be done in L2 can be done in super Hilbert space. In addition, however, it is possible to have a time operator and thus to base relativistic quantum mechanics on covariant four-dimensional commutation relations.