Wightman Axioms, Analyticity, and the Reeh-Schlieder Theorem

Professor Wayne Polyzou; Department of Physics and Astronomy, University of Iowa

I plan to give a brief discussion of the Wightman axioms.

The Wightman functions are vacuum expectation values of quantum fields.  They represent the kernel of a Lorentz covariant pre-inner product.  Because intermediate states satisfy a spectral condition, they have an analytic continuation to a region with complex times (called the tube).  This domain of analyticity can be extended using complex Lorentz transformations (called the extended tube).  The extended tube contains spacelike separated points, which allows the fields to be permuted, extending the domain of analyticity (the extended permuted tube).  Reeh-Schlieder Theorem follows from analyticity on open sets of the boundary of the domain of analyticity.
It means that the full Wightman functions can be constructed from the values of these distributions on an open set. These analytic properties are important for the connection to the Euclidean axioms and general theorems like the PCT theorem.  I will provide some details on how these analytic properties arise.

To participate in the seminar remotely via Zoom, go to https://uiowa.zoom.us/j/99570315915