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<p>In thermal quantum field theory, the global Liouvillian (the generator of time translations) is passive. How is this reflected in the properties of its local density, a quantum field? We propose that the locally averaged density is bounded below, but not above, with respect to the noncommutative <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(L^4\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>L</mi> <mn>4</mn> </msup> </math></EquationSource> </InlineEquation> norm. This is analogous to the known quantum energy inequalities in the vacuum situation. Our examples include thermal equilibrium on Minkowski space, and the Unruh effect on the Rindler wedge, both for the real scalar free field.</p>

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Quantum \(L^p\) Inequalities in Thermal States

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年8月1日

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  • Henning Bostelmann,
  • Daniela Cadamuro,
  • Leonardo Sangaletti

摘要

In thermal quantum field theory, the global Liouvillian (the generator of time translations) is passive. How is this reflected in the properties of its local density, a quantum field? We propose that the locally averaged density is bounded below, but not above, with respect to the noncommutative \(L^4\) L 4 norm. This is analogous to the known quantum energy inequalities in the vacuum situation. Our examples include thermal equilibrium on Minkowski space, and the Unruh effect on the Rindler wedge, both for the real scalar free field.