College of Liberal Arts & Sciences

# Math Physics Seminar

**Abstract:**

In scalar case, the existence of quantum field is equivalent to the existence of a Euclidean-invariant reflection positive measure on the Schwartz space tempered distributions. Stochastic quantization is realized as a method of obtaining the measure dμ(ϕ) on Schwartz distribution space as the limit λ ⤑ ∞ of sequence of measures dμλ(ϕ) defined by a dynamical equation for a field subjected to a random force. Martin Hairer investigated random fields by studying non-linear stochastic partial differential equation with a ``white noise'' driving term. In this talk we will investigate the question whether a quantum field can be obtained from the measure on the solution induced by the stochastic driving term.

*Recordings of the Zoom Session will be available a few hours later in this folder (https://uicapture.hosted.panopto.com/Panopto/Pages/Sessions/List.aspx#folderID=%2236fb4141-c398-421f-8161-ae2e016d2b2d%22). You may be asked to log in with your HawkID and password first, then you can find the date of the session you want to watch, and click the session title to watch the recording.