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 fellow Physics enthusiasts, I am an aeronautical engineering graduate (Bachelor's) who is interested in Physics and Mathematics, and I have been re-learning all the basics. I wanted to join a science forum, especially one dedicated to Physics and maths, to apply these subjects to my engineering studies. I hope to learn a lot through this forum. Thank you for your warm welcome.
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