The information in a wave


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May 5, 2020 10:00 am - 11:00 am
via Zoom Video Conferencing

Roberto Longo - University of Rome Tor Vergata

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 wavepacket 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 spacetimeW. 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 vectorof 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.

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