Rabinowitz action functional is invariant under the circle action obtained by reparametrising loops.
Taking equivariant homology with respect to the reparametrisation action leads to equivariant Rabinowitz Floer homology. The classifying space for the circle is infinite projective space whose cohomology ring is isomorphic to polynomials of one variable of degree two. Replacing polynomials by Laurent polynomials leads to Tate Rabinowitz Floer homology. Tate Rabinowitz Floer homology has the structure of a module over the group ring of the integers. This module structure gives rise to a quantisation condition. In the lecture we compute spectral numbers in some examples and show how they lead to Tate Rabinowitz quantized energy values.