Microcausality without Lorentz invariance
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 Lorentz-breaking states. We restrict to spatially homogeneous and isotropic state...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2025-07-01
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| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1007/JHEP07(2025)188 |
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| Summary: | 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 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 → $$ \overrightarrow{k} $$ ) 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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| ISSN: | 1029-8479 |