My 2 cents: anomalies concerning gauge symmetries (or better: gauge redundancies) are all about degrees of freedom. In QED you start out classically with a spin-1 field having 2 physical degrees of freedom, and after quantization you want to keep it that way. That means you want to retain the...
The gematria of Genesis 1:1 reveals its value as 2701, who's prime factorization is 37x73, two mirror prime numbers containing the trinity and divine wholeness who's ordinals 12 and 21 are also mirror numbers.
Grtz grtz God
See also Leibniz's integral rule:
https://en.wikipedia.org/wiki/Leibniz_integral_rule
or the lecture notes
https://kconrad.math.uconn.edu/blurbs/analysis/diffunderint.pdf
wheren also counterexamples are discussed.
Well, there are some physicists who think you should go to the philosophy department if you ask about ontology. In my experience quite some physicists care more about calculation than interpretation and worse, they'll use faulty philosophy to justify that attitude.
Yeah, I recognize that. When I followed a course on QFT, I just wanted to be able to calculate some amplitudes and understand renormalization. Only after that course the questions kicked in: why are spacetime suddenly mere labels? Don't we have a position operator anymore? What's the ontology of...
I once wrote some personal notes on QFT about stuff I was bothered with; the basics of i-epsilon prescriptions, contour integration, Planck units and renormalization; things like that. Somehow you'd say somebody wrote a textbook with this kind of techniques used in QFT. But apparently it's...
For people who like the ancient near East: check out the Digital Hammurabi channel of Joshua Bowen and Megan Lewis (Lewis' podcast with Bart Ehrman is also excellent by the way). They also give courses on languages like Akkadian.
One of those channels which make me doubt my career choice as a...
Consuming way too much alcohol, listening to Queen and Led Zeppelin, being frustrated by not understanding Hawking's Brief history of time, reading Brian Greene on string theory and spending most of my time playing the piano.
Leaving no room for school, now I think about it.
Just to add: in my experience good students are not good researchers per se. Getting good marks on exams is a different skill than doing independent research. And the question is whether you're using the politics merely as an excuse.
If you prove that the first derivative of f(x)=x^2 vanishes in x=0, does this mean it vanishes in every point?
You can change your grid such that the point formarly known as x=0 is moved to x=b such that now f'(x=b) becomes 0, but this is only in this particular point again.
I'd say they're roughly at the same level. What you miss out on depends on what you want to do with it. (I'm more familiar with P&S and Schwartz.) But looking at the content I'd say they're all good; just see which style suits you best.