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Microcausality without Lorentz invariance

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arxiv 2502.04215 v2 pith:5RU5ZHX3 submitted 2025-02-06 hep-th

Lam Hui , Alberto Nicolis , Alessandro Podo , Shengjia Zhou This is my paper · ORCID
classification hep-th
keywords statesmicrocausalitycommutatorsconditionsderivefieldfunctionsinflationary
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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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Cited by 7 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. The Lorentzian geometry of relaxation

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    Causality forces purely relaxational dispersion relations to follow spacelike trajectories on the Lorentzian {iω,ik} plane, producing universal bounds on diffusivity, viscosity, time-dilation deviations, and hydrodyna...

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  5. Probabilistic Causality from Graviton Fluctuations

    hep-th 2026-06 unverdicted novelty 7.0 of 10

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    hep-th 2026-05 unverdicted novelty 7.0 of 10

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  7. Propagator positivity bounds for cosmological correlators

    hep-th 2025-12 conditional novelty 7.0 of 10

    An infinite tower of two-sided positivity bounds constrains the EFT coefficients of heavy fields on de Sitter, ruling out correlators with no unitary/causal UV completion.

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