Expressing entropy globally in terms of (4D) field-correlations

7th International Conference on Gravitation and Cosmology

Sorkin, R.D.^1,2

Perimeter Institute, 31 Caroline Street North, Waterloo, ON N2L 2Y5, Canada^1

Department of Physics, Syracuse University, Syracuse, NY 13244-1130, United States^2

关键词: Event horizon;    Gaussian form;    Reduced-density matrix;    Scalar fields;    Space-time character;    Space-time correlation function;    Space-time region;    Spacetime;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/484/1/012004/pdf
DOI  :  10.1088/1742-6596/484/1/012004

来源: IOP

【 摘 要 】

We have expressed the entropy of a scalar field directly in terms of its spacetime correlation function, assuming that the higher correlators are of Gaussian form. The resulting formula associates an entropy to any spacetime region, and when this region is globally hyperbolic with Cauchy surface then the entropy can be interpreted as the entropy of the reduced density-matrix belonging to the Cauchy surface. One acquires, in particular, a new expression for the entropy of entanglement across an event-horizon. Thanks to its spacetime character, this expression makes sense in a causal set as well as in a continuum spacetime.