Roberto Longo
(University of Rome Tor Vergata)
December 15, 2021
15:30
(CET)
Organized by Europe GNCG Seminar.

## The Modular Hamiltonian and Classical/Quantum Information Theory

I present the key concept of entropy of a vector in a complex Hilbert space with respect to a real linear subspace. The entropy is related to the Tomita-Takesaki modular theory. I compute the local entropy of a classical or quantum wave packet. In particular, I provide the formula for the local modular Hamiltonian in the free, scalar massive Quantum Field Theory, and of the associated entropy density. The Yukawa potential here appears intrinsically. Several consequences, as holographic or entropy/energy (in-)equalities, naturally emerge in this framework. If time permits, I will explain the relation with the Quantum Null Energy Condition.