Search results

  1. L

    Basic metric diagonalization questions

    I understand it is always possible to diagonalize a metric to the form diag[1,-1,\dots,-1] at any given point in spacetime because the metric is symmetric and we can always re-scale our eigenvectors. But is this achievable via a coordinate transformation? That is, would the basis...
  2. L

    Källen-Lehmann Representation

    I have two basic questions about the full propagator (2-point function) in QFT. Am I correct that for a scalar field, it is \frac{iZ}{p^{2}-m^{2}+i \epsilon} + \int_{m^{2}}^{\infty} dX \frac{\rho[X]}{p^{2}-X+i \epsilon} ? (1) Is this form of the propagator a feature of _quantum_ field theory...
  3. L

    What is a bifurcation surface and a binormal vector?

    I've been reading Wald's book on GR as well as his article "Thermodynamics of Black Holes" in Living Reviews in Relativity about the definitions of mass and energy in GR and the concepts of entropy and temperature of black holes. I keep coming across the words "bifurcation surface" and...
  4. L

    On the uniqueness of QED

    I've always been a little puzzled by this breaking of unitarity. What sort of interactions would break unitarity? How exactly is unitarity broken by these interaction terms? I'm trying to get an understanding why unitarity can be broken at all. Do we have an analogous situation in QM? It is...
  5. L

    On the uniqueness of QED

    Could you explain what you meant by the above statements?
  6. L

    Vacuum Polarization - Why invoked?

    You asked how vacuum polarization would affect the propagation of photons from point A to point B, and what I wrote was to describe one specific instance of where the exchange of virtual particles - what I interpret as your "vacuum polarization" - has an observable effect.
  7. L

    Vacuum Polarization - Why invoked?

    We can ask the following question: Do photons ever interact with each other? When we cross two laser beams, do we get any light that gets kicked out sideways or do something funny? Or, in Star Wars lingo, are light savers really possible? If Maxwell's equations are the exact laws of nature...
  8. L

    Stress-Energy Tensor from Lagrangian: Technical Question

    Juan: could you explain briefly what's the advantage of using +2 in GR problems?
  9. L

    Stress-Energy Tensor from Lagrangian: Technical Question

    Physics Monkey - thank you for taking the time to reply. I think you've cleared up my confusion.
  10. L

    Stress-Energy Tensor from Lagrangian: Technical Question

    This popcorn you consumed - I appreciate your offer, though I'd politely decline - what's more pressing is, could you advise me, what exactly is its Lagrangian, or "world function", as D. Hilbert calls it? And would you recommend taking the derivative with respect to upper or lower index metric...
  11. L

    Stress-Energy Tensor from Lagrangian: Technical Question

    I still don't fully understand how to go from \vec{E} = -\frac{\partial \vec{A}}{\partial t} - \nabla A^{0} to E_{i} = \partial_{i} A_{0} - \partial_{0} A_{i} In the first line, should it be a A^{0} or A_{0}? And when I convert to component notation should I write...
  12. L

    Stress-Energy Tensor from Lagrangian: Technical Question

    Thank you for your clarification - again it is very helpful. It is rather interesting you brought up the electromagnetic potential, because I started thinking about all this due to my trying to get the correct stress-energy tensor out of Maxwell's "free" lagrangian \mathcal{L} = -\frac{1}{4}...
  13. L

    Stress-Energy Tensor from Lagrangian: Technical Question

    Thank you for your reply, Physics Monkey. It was helpful. It seems what you're saying is that \frac{\partial}{\partial g_{\mu \nu}} = -g^{\alpha \mu} g^{\beta \nu} \frac{\partial}{\partial g^{\alpha \beta}} The way I got this was to consider \frac{\partial}{\partial g_{\mu \nu}}...
  14. L

    Stress-Energy Tensor from Lagrangian: Technical Question

    Stress-Energy-Momentum Tensor from Lagrangian: Technical Question I've been reading about how to generate the stress-energy-momentum tensor T^{\mu \nu} from the action S = \int d^{4}x \sqrt{|g|} \mathcal{L} T^{\mu \nu} = \frac{2}{\sqrt{|g|}} \frac{\partial}{\partial g_{\mu \nu}} \left(...
  15. L

    Introducing LaTeX Math Typesetting

    Norman Could you explain how to use this simple_wick.tex file? I don't understand the example given at all. Thanks!
  16. L

    Photon propagator in an arbitrary gauge

    \left(\Box g_{\mu\nu} - \Big(1-\frac{1}{\xi}\Big) \partial_\mu \partial_\nu \right) A^\nu (x) = 0 You simply need to invert the quadratic differential operator above in momentum space (aka Fourier space). In momentum space the photon kinetic term looks like \int \frac{d^{4}k}{(2...
  17. L

    A Horrible Gravity Question

    This may be a little too strong a statement, as though HR follows very naturally from GR and QFT. As long as we have not observed directly radiation from black holes we cannot assume it has to exist. I've also recently come across theoretical objections to the existence of black hole...
  18. L

    Question about epsilons that occurs in calculating beta functions in QFTs w dim reg

    Question about epsilons that occur in calculating beta functions in QFTs w dim reg In deriving the beta function of, say, QED using dimensional regularization we get the relation (up to 1 loop) \beta[e] = - \frac{\epsilon}{2} e - e \frac{d ln[Z_{e}]}{d ln[\mu]} \quad (1) and Z_{e} = 1...
  19. L

    What is the physical mass and coupling?

    By the way I now have fair confidence that this funny mass dependence is correct; Cheng and Li's problem book on gauge theory got it wrong and I asked the authors if it was a mistake and Li replied saying yes.
  20. L

    What is the physical mass and coupling?

    Given any quantity A and some small \epsilon << 1. We have A^{\epsilon} = exp[ Log[ A^{\epsilon} ] ] = exp[ \epsilon Log[ A ] ] \approx 1 + \epsilon Log[ A ] where the last step just comes from Taylor expanding the exponential.
  21. L

    What is the physical mass and coupling?

    Peskin (A.44) says \int \frac{d^{4-2\epsilon}l}{(2 \pi)^{4-2\epsilon}} \frac{1}{(l^{2}-\Delta)^{n}} = \frac{(-1)^{n}i \Gamma[n-(2-\epsilon)]}{(4 \pi)^{2-\epsilon} \Gamma[n]} \left( \frac{1}{\Delta} \right)^{n-(2-\epsilon)} If we identify k = l, n = 1, and \Delta = m^{2}, we see that the...
  22. L

    What is the physical mass and coupling?

    This dimension issue is bugging me. I'll post my steps and if anyone cares to follow thru, let me know if you spot an error. We know that \mathcal{L} = \frac{1}{2} \partial_{\mu} \phi \partial^{\mu} \phi - \frac{1}{2} m^{2} \phi^{2} - \frac{\lambda \mu^{\epsilon}}{3!} \phi^{3} must...
  23. L

    What is the physical mass and coupling?

    Not really: it remains unhappy because Log[{\mu}/{m^{2}}] = \frac{1}{2} Log[{\sqrt{\mu}}/{m}], and so we're just exchanging mass/mass^{2} for \sqrt{mass}/mass.
  24. L

    How to compute the number of loops in a Feynman diagram?

    Under the "Quantum Physics" forum link it says "Quantum Mechanics and Field Theory" - that's why I posted my questions here. Anyone who knows some QFT would know that these questions do form the bulk of the QFT experience. Renormalization, for instance, is all about the technicalities - how...
  25. L

    What is the physical mass and coupling?

    I need to worry about every factor of -1's, \pi's and i's if I want to learn this stuff properly - this is my goal. By pole terms do you mean the 1/{\epsilon}'s? I'm doing dim reg, so my integrals live in 4-2{\epsilon} spacetime dimensions.
  26. L

    How to compute the number of loops in a Feynman diagram?

    Do you mean my thread was moved because \lambda \phi^{3} is not a physical theory? :smile:
  27. L

    How to compute the number of loops in a Feynman diagram?

    In doing my \phi^{3} theory I didn't know exactly how to count the number of loops in a diagram given the number of vertices, internal and external lines. Is there a general algorithm in doing this? What if we have more than one interaction vertex (e.g. the Standard Model)? PS. What does it...
  28. L

    What is the physical mass and coupling?

    I have a very basic question about exactly how to match the experimentally measured masses and coupling constants to the parameters in the lagrangian density in a given QFT. Let me specialize to a particular theory and perhaps people here can help me out. I've just computed the tadpole and...
  29. L

    Why Neutron Does Not Decay

    I'm seeking what the underlying mechanism is that's preventing the decay. If it's kinematical, as claimed, I'm trying to see if there's an easy way to understand why the mass of the neutron would be decreased sufficiently when bound inside a nucleus to disallow its decay.
  30. L

    Why Neutron Does Not Decay

    I'm not sure if this is an explanation. Why would a neutron get lighter when bound to a nuclei, if this were really the case?
Top