What are the latest developments in discrete Quantum Field Theories?

Skoceko
I have been interested in physics for a very long time. Initially in high school celestial mechanics and soon afterwards quantum mechanics. During my chemistry studies I specialized in quantum chemistry at the end of my bachelor and continued to do a Bachelor and Master in pure Mathematics, with a specialization in stochastics and PDE (especially Schrödinger Operators).

Recently I started to look into Quantum Field Theories and my questions will be mostly around that topic. I started writing in math style a "book" (see my github) about a discrete version of Quantum electrodynamics in 2d. I could not find many good sources so maybe much of my work is already published, also I write in german.
 
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Hello there, and nice to meet all of you! My name is Olga, I am from Russia. I have a PhD in laser physics, and I work at the local university. I study chalcogenide lasers. I am a pure experimentalist, and I love working with my hands, et cetera, and I do math only when I have to. Sometimes I work with biologists. I do nothing exciting in research, and after my defence, I hardly can call myself a scientist because we have a lack of financial support, and most of my time I spend on teaching...

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