An intuitive construction of modular flow
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13130_2023_Article_22389.pdf
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734.35 KB
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4f9163cb1049046dd1b660798df12fee
Author(s)
Sorce, Jonathan
Date Issued
December 12, 2023
Publisher
Springer Berlin Heidelberg
Citation
Journal of High Energy Physics. 2023 Dec 12;2023(12):79
Version
Final published version
Abstract
The theory of modular flow has proved extremely useful for applying thermodynamic reasoning to out-of-equilibrium states in quantum field theory. However, the standard proofs of the fundamental theorems of modular flow use machinery from Fourier analysis on Banach spaces, and as such are not especially transparent to an audience of physicists. In this article, I present a construction of modular flow that differs from existing treatments. The main pedagogical contribution is that I start with thermal physics via the KMS condition, and derive the modular operator as the only operator that could generate a thermal time-evolution map, rather than starting with the modular operator as the fundamental object of the theory. The main technical contribution is a new proof of the fundamental theorem stating that modular flow is a symmetry. The new proof circumvents the delicate issues of Fourier analysis that appear in previous treatments, but is still mathematically rigorous.
MIT Department
Massachusetts Institute of Technology. Department of Physics
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Creative Commons Attribution
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DOI of Published Version
https://doi.org/10.1007/JHEP12(2023)079
