Connes' trace.. but what is the operator ?¿¿

zetafunction

What is the operator inside the Connes' approach to RH ??, he gave a trace but never says what operator is or gives or write down any operator or dynamicals system for this operator

i am talking about the paper

http://www.math.osu.edu/lectures/connes/zeta.pdf

shouldn't he prove that his traceor that the functional determinant of his operator is just the Riemann Zeta function on the critical line ??.