= Positive energy representation of the loop group of U(1)
{title2=$R_t\pi(g)R_t^*=\pi(g(e^{it}\,\cdot))$}
Such a continuous <projective unitary representation> admits strongly continuous rotations whose self-adjoint generator is bounded below and whose adjoint action rotates the loops. In the basic fermionic construction, integer one-particle modes are filled below zero. The rotation energy counts nonnegative particle energies and positive hole energies. It has finite-dimensional integer eigenspaces and implements circle rotations. Tensor products give higher nonnegative integer levels.
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