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  1. BruceW

    Faithful representation

    Hello everyone! I've been learning some basic group theory (I'm new to the subject). And I had a (hopefully) fairly simple question. OK, so a 'faithful representation' is defined as an injective homomorphism from some group G to the Automorphism group of some object. Let's call the object S for...
  2. BruceW

    Lagrangian density of Newtonian gravity

    Hi everyone! I've been thinking about a certain problem for a while now. And that is a Lagrangian formulation of Newtonian gravity. I know there is a Lagrangian formulation for general relativity. But I was hoping to find a Lagrangian for Newtonian gravity instead (for some continuous mass...
  3. BruceW

    Trying to understand Gateaux differential

    Hi everyone! I've been trying to get my head around the Gateaux differential. (or derivative, however it is called). So anyway, I've seen it defined like this: \lim_{\tau \rightarrow 0} \frac{F(u + \tau \psi) - F(u)}{\tau} where the function ##F## takes ##X## to ##Y## (which are both locally...
  4. BruceW

    Mass eigenstates of the leptons

    Hi everyone, my question seems pretty simple, but I couldn't find any answers. OK, so the neutrino flavour eigenstates are different to the neutrino mass eigenstates. And this is why neutrino oscillation is possible. But for the charged leptons (the electron, muon and tauon) the mass...
  5. BruceW

    Is Euclidean space an affine space?

    Hi everyone, I have a question that I'm not sure about. I wanted to know if it is standard to think of Euclidean space as a linear vector space, or a (more general) affine space? In some places, I see Euclidean space referred to as an affine space, meaning that the mathematical definition of...
  6. BruceW

    Extrinsic thermodynamic variable confusion

    Hi all, Something has been troubling me. To begin with, I have never been certain about this concept of 'extrinsic' thermodynamic variables. I mean, they don't have to be linear with system size, right? They just need to increase with system size? And also, I have a specific 'example problem'...
  7. BruceW

    Timelike v. spacelike, is it arbitrary?

    EDIT: Split from https://www.physicsforums.com/showthread.php?t=704345 after a bit of searching, I found "An introduction to general relativity and cosmology" jerzy plebanski, andrzej Krasinski, where they don't use different terms for proper time and proper length. They just use the word...
  8. BruceW

    Limits of integral after substitution

    Hi everyone, I am having a 'crisis of faith' in how the limits of an integral should change when you make a substitution for the variable involved. Especially when using a sinusoid substitution, since the sinusoidal functions are not 1-to-1 functions. Anyway, let's use an example integral...
  9. BruceW

    Laurent series - where does f(z) need to be holomorphic?

    Hey everyone, I've got a question that might be interesting to those of you that enjoy maths. Note: I only did a physics degree, so I have never really done analysis in the proper way a mathematician has. But I am eager to learn about more rigorous maths. Right, so for a Laurent series about a...
  10. BruceW

    Quantum operator derivation

    Hi all! I was reviewing some basic quantum mechanics, and I was trying to 'derive' the equation -i \hbar \frac{\partial}{\partial x} \psi_{(t,x)} = <x| \hat{P} | \psi > using the commutator relation, and the form of the identity operator. OK, I know that the proper, mathematical way to prove the...
  11. BruceW

    EM tensor invariants

    Hey everyone I was looking up the EM tensor on wikipedia, and they mention two invariants. There is the obvious one - The Lorentz invariant B^2- \frac{E^2}{c^2} And there is also the product of the EM tensor with its dual, which they call the pseudoscalar invariant: \frac{1}{2}...
  12. BruceW

    Power dissipation in parallel circuit

    Right, so I was going over some old (basic) electromagnetism principles (to make sure it doesn't all fall out of my head). And I was thinking about two resistors in parallel, assuming some constant dc voltage across them. And I was thinking about the power dissipated by this simple circuit. And...
  13. BruceW

    LaTeX Latex problem

    The command \vec{}, whenever I see it in posts, comes out as a small square box, instead of the arrow above the letter, as it should. All other latex commands seem to work fine. I think the problem might be to do with the settings on my browser (i'm using chrome). I was wondering if anyone...
  14. BruceW

    Gravitational waves predicted by Einstein

    I've read a newspaper article which claims: "If the search for gravitational waves succeeds, then Einstein's theory of general relativity may have to be revised" But I thought that Einstein predicted gravitational waves, so surely if they are found, it would confirm general relativity. I don't...
  15. BruceW

    Classical light diffraction round corner

    I know how photons are diffracted round a corner in quantum mechanics. But is there also an explanation in classical electromagnetic theory (i.e. by Maxwell's laws?) Imagine there was an EM wave travelling purely normal to a slab of material which is highly attenuating, but which has a small...
  16. BruceW

    Square roots

    I understand the basics of raising numbers to powers of whatever, but i've been wondering: When you square a number then square root it, you end up with plus or minus the original number. (i.e. 5 times 5 gets 25, then root gets 5 or -5). But using the rules of raising numbers to powers of...
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