2025/02/06 by Hui, Lam, Nicolis, Alberto, Podo, Alessandro +1 · 3 citations
#FOS: Physical sciences #High Energy Physics - Theory (hep-th)
paper · doi:10.48550/arxiv.2502.04215
Microcausality -- the vanishing of commutators outside the lightcone -- is a fundamental property of relativistic quantum field theories. We derive its implications for two-point functions of scalar operators on \it Lorentz-breaking states. We restrict to spatially homogeneous and isotropic states, at zero and finite temperature, such as finite-density states of matter and primordial inflationary states. In a mixed (t, k ) representation, we find certain analyticity and exponential boundedness conditions, which we verify in a variety of examples. Crucially, we discuss how our conditions can be tested within the regime of validity of Lorentz-breaking low-energy effective field theories, clarifying the role of the group velocity of low-energy excitations. In the cosmological case, we derive a positivity condition on an EFT coefficient in an inflationary background. Lastly, we comment on how microcausality can be used to constrain higher-point correlation functions, via suitable nested commutators.