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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2502.04215 |
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| _version_ | 1866909700624220160 |
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| author | Hui, Lam Nicolis, Alberto Podo, Alessandro Zhou, Shengjia |
| author_facet | Hui, Lam Nicolis, Alberto Podo, Alessandro Zhou, Shengjia |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_04215 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Microcausality without Lorentz invariance Hui, Lam Nicolis, Alberto Podo, Alessandro Zhou, Shengjia High Energy Physics - Theory 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. |
| title | Microcausality without Lorentz invariance |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2502.04215 |