Phase Space Methods in Quantum Mechanics and Weak Values.

          @misc{ pirsa_PIRSA:16060047,
            doi = {10.48660/16060047},
            url = {https://pirsa.org/16060047},
            author = {Lobo, Gus},
            keywords = {Quantum Foundations},
            language = {en},
            title = {Phase Space Methods in Quantum Mechanics and Weak Values.},
            publisher = {Perimeter Institute},
            year = {2016},
            month = {jun},
            note = {PIRSA:16060047 see, \url{https://pirsa.org}}
          }
          

Abstract

Phase space methods are ubiquitous in quantum mechanics. From the Weyl-Wigner Moyal formalism to coherent states and discrete phase spaces we see the imprints of the classical world again and again. In this presentation, we address one of two major developments introduced by Aharonov and his collaborators: The concept of weak values that stems from a time-symmetric view of quantum physics. We look at the weak measurement through two distinct geometric frames: The geometry of the measuring apparatus and the geometry of the measured system. We …nalize with some brief comments on the second major conceptual due to Aharonov and collaborators: the theory of modular variables and how Schwinger´s discrete phase space structure helps to shed light on it. We conclude then with the following mantra: It´ s all about phase space.