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...
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...
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...
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...
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.
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...
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...
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...
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}...
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}}...
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(...