Kolloquium Wilhelm Killing: Prof. Dr. Roberto Longo (Rom): The information in a wave
Thursday, 16.01.2020 16:30 im Raum M5
Suppose that some information is transmitted by an undulatory signal. In Classical Field Theory, the stress-energy tensor provides the energy-momentum density of the wave packet at any time. But, how to measure the information, or entropy, carried by the wave packet in a certain region at given time?
Surprisingly, one can answer the above (entirely classical) question by means of Operator Algebras and Quantum Field Theory. In fact, in second quantisation a wave packet gives rise to a sector of the Klein-Gordon Quantum Field Theory on the Rindler spacetime W. The associated vacuum noncommutative entropy of the global von Neumann algebras of W is the entropy of the wave packet in the wedge region W of the Minkowski spacetime. One can then read this result in first quantisation via a notion of entropy of a vector of a Hilbert space with respect to a real linear subspace.
I give a path to the above results by an overview of some of basic results in Operator Algebras and Quantum Field Theory and of the relation with the Quantum Null Energy Inequality.