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<p>We revisit the TFD formulation for finite-temperature field theory and demonstrate its fundamental role in grasping key aspects of real-time finite-temperature field theory. Specifically, we demonstrate that the general unitary <Emphasis Type="BoldItalic">SU</Emphasis><b>(1,1)</b> formulation of TFD, in which the conjugation rules are redefined, is consistent with the GNS construction and Tomita-Takesaki theory. We calculate the <Emphasis Type="BoldItalic">SU</Emphasis><b>(1,1)</b> thermal propagator and show that the KMS condition is independent of the choice of the <Emphasis Type="BoldItalic">SU</Emphasis><b>(1,1)</b> parameters.</p>

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General Unitary SU(1, 1) Formulation of TFD and its Relation to Tomita-Takesaki Theory

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年6月20日

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  • Alexandre L. Gadelha,
  • Daniel L. Nedel,
  • Carlos R. Senise Jr.

摘要

We revisit the TFD formulation for finite-temperature field theory and demonstrate its fundamental role in grasping key aspects of real-time finite-temperature field theory. Specifically, we demonstrate that the general unitary SU(1,1) formulation of TFD, in which the conjugation rules are redefined, is consistent with the GNS construction and Tomita-Takesaki theory. We calculate the SU(1,1) thermal propagator and show that the KMS condition is independent of the choice of the SU(1,1) parameters.