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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I am retired with a scientific background in Mathematics and Physics though I quit Academia after graduation. Recently, my interest has revived and I have started to review what I knew before and learn new stuff. My interests are in Physics and Mathematical Physics. I hope I can find answers to some of my questions here and perhaps in the future, I can also answers some questions. How have I arrived here? During the past two months, I have been doing some online research to find the best...