The massive modular Hamiltonian

Abstract: A solution of the Klein-Gordon equation can be viewed as a signal carried by a classical wave packet, or as the wave function of a quantum particle, or as a coherent state in Quantum Field Theory. Our recent work concerns the definition, computation and interpretation of the local entropy of this object and its relation to quantum energy inequalities. The Operator Algebraic approach, in particular the Tomita-Takesaki modular theory, provides a natural framework and powerful methods for our analysis. In this talk, I will discuss part of the general ground for our analysis and some key results, in particular the solution of an old problem in QFT: the description of the modular Hamiltonian associated with a space ball B in the free scalar massive QFT; this sets up the formula for the entropy density of a real wave packet.

statistical mechanicsmathematical physicsanalysis of PDEsprobability

Audience: researchers in the topic

Analysis, Quantum Fields, and Probability

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Recorded talk are available on youtube.