What topics can independent scientists explore in math and physics?

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Ken Miller
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My name is Ken Miller. I'm an independent-study person, 67 years of age. I retired a few years ago from an electrical engineering job, and recently got interested in pursuing (for my own fun) some aspects of math and physics that I didn't cover in school or work: group theory, calculus of variations, relativity, advanced mechanics, quantum theory, and others (including digging deeper into electromagnetic theory than I did either in school or work). Without others around me to consult, it's pretty easy for me to get stuck on a problem or even a concept, so I'm excited about finding Physics Forums--hurray! I will probably be mostly a beneficiary of others' wisdom for some time, but hope I can develop into a help for others at some point.
 
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Hi Ken Miller. :welcome:
 
Hello everyone, I was advised to join this community while seeking guidance on how to navigate the academic world as an independent researcher. My name is Omar, and I'm based in Groningen The Netherlands. My formal physics education ended after high school, but I have dedicated the last several years to developing a theoretical framework from first principles. My work focuses on a topological field theory (which I call Swirl-String Theory) that models particles as knotted vortex...
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