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  1. Infrared

    Schools About to Start college but don't know what to do!

    Well, the title isn't quite right. I want to study (pure) math, but this probably isn't the most employable STEM major out there. So, since I do plan on pursuing a BA in mathematics, I've also been thinking about what I can do/take additionally in the coming years that would allow for avenues...
  2. Infrared

    Conformal Flatness of Lorentzian 2-Manifolds

    I have seen it stated that any Lorentzian 2-manifold is locally conformally flat; in what sense is it local? Is there a way to show this explicitly?
  3. Infrared

    Resurrect PF Chess?

    There used to be a chess feature on this site. Unfortunately, this existed and was eliminated well before I became a member. I enjoy playing chess and from what I understand, so do many other members here. Is there a possibility of bringing back PF chess? I think it would be a great way for...
  4. Infrared

    Maxwell's Equations in Curved Space-time

    Can one show that strict charge conservation ##\nabla_{a}J^{a} = 0## follows directly from ##\nabla_{a}F^{ab} = 4\pi J^{b}## alone? Also, how does ##d^{\star}F = 4\pi ^{\star}J## follow directly from that same equation where ##\star## is the Hodge dual operator?
  5. Infrared

    Matrix exponential in QM

    In class, my teacher was motivating Schrodinger's Equation, but there is one step that I do not understand or even have intuition for. I'll give the argument leading up to the step I do not understand for context. Let \hat{U}(t) be the operator that gives the wave function after time t, given...