Shadi Tahvildar-Zadeh – Rutgers University
Date/Time/Location
Thursday, November 6th, 2025, 12:10 pm; Hill Center 705
Quantum Ping-Pong
I will survey the results of several joint works with M. Kiessling, L. Frolov, and others, on the quantum-mechanical treatment of Compton scattering in one space dimension, in which photons are treated as particles on equal footing with electrons. This is achieved through a certain relativistic extension of the framework proposed in 1927 by de Broglie and 25 years later again by Bohm, and relies on our ability to describe (in any number of space dimensions) not just the electron, but also the photon, as a point particle whose motion is guided by a relativistic quantum mechanical wave function, one that possesses a conserved time-like future-directed probability current.
The interaction between the two particles is implemented via a Lorentz-invariant no-crossing-of-paths boundary condition for the multi-body, multi-time wave function of the system. I will first outline the proof of global well-posedness of the initial-boundary value problem for the 1 electron-1 photon system. I will then report on our recent extension of this work to a quantum-mechanical three-body system, still in one space dimension, comprised of one photon situated between two electrons. The electrons do not interact directly, but only via the photon bouncing between them. The corresponding initial-boundary value problem is again proven to be well-posed, and we show that the unique solution can be represented by a convergent infinite sum of Feynman-like diagrams, each one corresponding to the photon bouncing between the two electrons a fixed number of times.