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arXiv · 1005.0760

Geometry of Schroedinger Space-Times II: Particle and Field Probes of the Causal Structure

Matthias Blau·Jelle Hartong·Blaise Rollier
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Abstract

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 the 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.

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Matthias Blau, Jelle Hartong, Blaise Rollier. 2010-05-05. Geometry of Schroedinger Space-Times II: Particle and Field Probes of the Causal Structure. https://doi.org/10.1007/jhep07(2010)069

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