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<p>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 <i>Lorentz-breaking</i> 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 (<i>t</i>, <InlineEquation ID="IEq1"> <EquationSource Format="MATHML"><math display="inline"> <mover accent="true"> <mi>k</mi> <mo stretchy="true">→</mo> </mover> </math></EquationSource> <EquationSource Format="TEX">\( \overrightarrow{k} \)</EquationSource> </InlineEquation>) 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.</p>

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Microcausality without Lorentz invariance

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年7月16日

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  • Lam Hui,
  • Alberto Nicolis,
  • Alessandro Podo,
  • Shengjia Zhou

摘要

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.