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arXiv · 2502.04215

Microcausality without Lorentz invariance

Lam Hui·Alberto Nicolis·Alessandro Podo·Shengjia Zhou
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Abstract

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 $(t, \vec k \, )$ 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.

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Lam Hui, Alberto Nicolis, Alessandro Podo, Shengjia Zhou. 2025-02-06. Microcausality without Lorentz invariance. https://doi.org/10.1007/jhep07(2025)188

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