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Mathematical and Theoretical Physics Seminar: S-matrix bootstrap: the space of Scattering matrices in 2 and 4 dimensions.

Event Type
Seminar/Symposium
Sponsor
The Physics Department
Location
Loomis 222
Date
Sep 15, 2022   1:00 pm  
Speaker
Martin Kruczenski (Purdue)
Contact
Janice Benner
E-Mail
jbenner@illinois.edu
Views
24
Originating Calendar
Physics - Mathematical and Theoretical Physics Seminar

Abstract: One of the main purposes of quantum field theory is to compute the scattering matrix (S-matrix) that describes collisions between particles. General assumptions on its properties determine the S-matrix of two scalar particles in terms of a set of analytic functions of one variable (in two dimensions) and two variables (in four dimensions).  Recently there has been some interesting developments in understanding the space of allowed S-matrices. In this talk I will discuss first the case of two dimensions where progress can be made using a combination of numerical tools from the theory of conic optimization and analytical tools from functional and complex analysis. The result is that the space is convex with a boundary that has vertices where interesting theories are found. When such distinguished point is located, the corresponding S-matrix follows numerically without any further input. Afterwards I will discuss recent ideas to extend this to 4 dimensions.   

 

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