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SUMMARY:Yidong Chen (UIUC)
DTSTART:20230411T193000Z
DTEND:20230411T203000Z
DTSTAMP:20260423T005722Z
UID:HET/48
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/HET/48/">Non
 commutative Poisson Random Measure and its Applications in AQFT and Quantu
 m Chaos</a>\nby Yidong Chen (UIUC) as part of Purdue HET\n\n\nAbstract\nOn
 e of the important problems in modern mathematical physics is to understan
 d quantization - both quantizing classical systems to quantum systems and 
 quantizing one-particle systems to many-body systems. Up to now\, the math
 ematical second quantization relies on the Gaussian functor and produces g
 eneralized free theories. Interactions are generally modeled by perturbati
 on theories (a la Glimm and Jaffe). In this talk\, we take a new approach 
 to second quantization by constructing a noncommutative analog of the clas
 sical Poisson random measure. This construction produces a functor which s
 hall be called Poissonization. The analog of correlation functions in this
  construction cannot be factorized into the sum of products of two-point f
 unctions. After we outlined the main ideas of Poissonization\, we will cle
 arly state the construction and its functorial properties. Moreover\, we w
 ill discuss the main properties of this construction\, emphasizing on its 
 versatility and physical relevance. Subsequently\, we will focus on two ma
 in areas of physical applications. On one hand\, we will discuss how Poiss
 onization can be used to produce examples of algebraic quantum field theor
 ies starting from the data of unitary representations of real semisimple L
 ie groups (single particles a la Weinberg). On the other hand\, we will di
 scuss how Poissonization can be used to rigorously calculate quantum infor
 mation quantities (e.g. relative entropy\, tripartite information\, out-of
 -time-order correlation etc.) in type III von Neumann algebras. In many to
 y examples\, these quantities have the right quanlitative behaviors as con
 jectured in physics literature. Lastly\, we will briefly discuss future di
 rections\, emphasizing on why we cannot yet claim to have constructed an i
 nteracting CFT in dimensions larger than 2 and how we can achieve this goa
 l using Poissonization.\n
LOCATION:https://researchseminars.org/talk/HET/48/
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