2012/05/14 by Sorkin, Rafael D. · 1 citation
#FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Quantum Physics (quant-ph)
paper · doi:10.48550/arxiv.1205.2953
We express the entropy of a scalar field phi directly in terms of its spacetime correlation function W(x,y) = , assuming that the higher correlators are of "Gaussian" form. The resulting formula associates an entropy S(R) to any spacetime region R; and when R is globally hyperbolic with Cauchy surface Sigma, S(R) can be interpreted as the entropy of the reduced density-matrix belonging to Sigma. 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.