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Some Results On Relative Entropy in Quantum Field Theory

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Abstract

We prove that the mutual information for vacuum state as defined by Araki is finite for general Dirac Quantum Fields in Minkowski spacetime of any dimension. In the case of two dimensional chiral conformal field theory (CFT) we use our previous results for the free fermions to show that for a large class of chiral CFT the mutual information is finite. We also provide a direct relation between relative entropy and the index of a representation of conformal net.

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Acknowledgements

Part of this work was done when I participated in Pitp 2018 at Institute for Advanced Study. I would like to thank E. Witten for making my visit possible and stimulating discussions, and R. Longo for helpful comments.

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Authors and Affiliations

  1. Department of Mathematics, Foshan University, Foshan, China

    Feng Xu

  2. Department of Mathematics, University of California at Riverside, Riverside, USA

    Feng Xu

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  1. Feng Xu
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Correspondence to Feng Xu.

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Communicated by Y. Kawahigashi

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Supported in part by NSF Grant DMS-1764157.

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Xu, F. Some Results On Relative Entropy in Quantum Field Theory. Commun. Math. Phys. 374, 1469–1482 (2020). https://doi.org/10.1007/s00220-019-03367-x

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