Geometry of Schrödinger space-times II: particle and field probes of the causal structure

Matthias Blau, Jelle Hartong, Blaise Rollier
2010 Journal of High Energy Physics  
We continue our study of the global properties of the z=2 Schroedinger space-time. In particular, we provide a codimension 2 isometric embedding which naturally gives rise to the previously introduced global coordinates. Furthermore, we study the causal structure by probing the space-time with point particles as well as with scalar fields. We show that, even though there is no global time function in the technical sense (Schroedinger space-time being non-distinguishing), the time coordinate of
more » ... he global Schroedinger coordinate system is, in a precise way, the closest one can get to having such a time function. In spite of this and the corresponding strongly Galilean and almost pathological causal structure of this space-time, it is nevertheless possible to define a Hilbert space of normalisable scalar modes with a well-defined time-evolution. We also discuss how the Galilean causal structure is reflected and encoded in the scalar Wightman functions and the bulk-to-bulk propagator.
doi:10.1007/jhep07(2010)069 fatcat:zkoki6t6xjgi5nciv6agbuscaq