Closed-Form Propagator of the Calogero Model

We present a generalization of the Mehler kernel, providing the exact analytic time evolution of the Calogero model that describes bosons or fermions propagating on the real line with inverse-square two-body interactions and harmonic confinement. The key to our result is a simple relation between the exact propagator of the Calogero model and a Baker-Akhiezer function, together with explicit combinatorial formulas for the latter function.