# Mathematical Physics Seminar

**Abstract:**

This will be a continuation of the talk from last week. In particular, we will discuss: (1) How the time reversal operator affects the representation of the Poincare Lie algebra on the Euclidean representation of the interacting quantum mechanical Hilbert space; (2) How reflection positivity dragoons the Schwinger two-point functions into having a particular form; and (3) How we can use said form of the two-point functions, together with the Carleman condition for the Stieltjes moment problem, to construct injection operators from the free Hilbert space into the fully interacting Hilbert space that simultaneously satisfy the Cook condition and preserve the Euclidean time ordering precept.