On the Weyl Symbols of Gaussian Semigroups

Explore a 44-minute lecture by Ralph Sabbagh from the University of California, Irvine, titled "On the Weyl symbols of Gaussian semigroups" presented at IPAM's Dynamics of Density Operators Workshop. Recorded on May 1, 2025, this talk begins with a generalized approach for constructing positive representations of quantum states with respect to quantum observables, inspired by recent interpretations of the Husimi function in Gaussian semigroups and its connection to the Wigner distribution. Delve into how each representation can be viewed as a smearing of its corresponding Wigner distribution, analogous to the Gaussian smearing that produces the Husimi function. Understand the importance of studying Weyl symbols for Gaussian semigroups that enable such smearing. The lecture covers key concepts including the Weyl functional calculus for unbounded self-adjoint operators and infinitesimal representations of Lie groups. For more information, visit the IPAM website at: https://www.ipam.ucla.edu/programs/workshops/workshop-ii-dynamics-of-density-operators/