623 reputation
39
bio website jacobi.luc.edu
location Chicago, IL
age
visits member for 3 years, 8 months
seen Oct 12 at 19:51

I'm an assistant professor of physics at a university in Chicago.


Aug
21
comment Vasiliev Higher Spin Theory and Supersymmetry
If this is the "Paul" that I think it is, hi and welcome to the site! If it's another Paul, I guess the same applies.
May
28
comment Tensor decomposition of $\partial_\mu A_\nu$
The symmetric, traceless part isn't gauge-invariant, so it shouldn't have the same sort of interpretation as the anti-symmetric part.
Jun
30
comment What experiment would disprove string theory?
Downvote for not answering the question.
Nov
13
comment Cubic term in gauge theories
I'm not sure why you'd do that. Do you know of some way of building a sensible F^3 theory?
Nov
12
comment Cubic term in gauge theories
Adding F^3 to the standard YM Lagrangian gives a non-renormalizable theory; you should only consider it as part of a low-dimensional effective theory. F^3 is the "least irrelevant" gauge-invariant operator for pure YM. So the low-energy expansion of some theory that holds at higher energies might have F^2 as the leading term and F^3 term as the first "correction".
Aug
12
comment Does the lack of modular nuclearity in string theory mean anything?
You don't even need quantum gravity to see that extensivity breaks down when gravity is important. Solve the Tolman-Oppenheimer-Volkov equation for a self-gravitating perfect fluid with equation of state $p=\kappa\rho$. This gives an energy density $\rho \sim r^{-2}$. Cut off the solution at some radial size $R$ and join it on to a solution that goes to zero at a finite distance. Relate the entropy density to the energy density using the EOS, integrate, and you get entropy $\sim R^{\frac{1+3\kappa}{1+\kappa}}$. The entropy of the self-gravitating object never grows faster than the area.
Aug
2
comment Cheat sheet of elementary particles
Here is a handy Eightfold Way reference chart from an undergrad class I taught on particle physics: cl.ly/8yhy . Of course, it will only be useful if you understand what it represents! There is a good review in "Introduction to Elementary Particles" by Griffiths.
Jun
3
comment Explicit Variation of Gibbons-Hawking-York Boundary Term
You're right -- simply preserving $n^{\mu}n_{\mu} = 1$ would only determine $\delta n^{\mu}$ up to a vector orthogonal to $n^{\mu}$. Instead, you should consider the definition of $n^{\mu}$. Let $\partial M$ be an isosurface of some coordinate $r$. Then $\alpha_{\mu} = \nabla_{\mu} r$ is orthogonal to the surface. Now normalize that vector to obtain: $$ n_{\mu} = \frac{\alpha_{\mu}}{\sqrt{g^{\nu\lambda}\alpha_{\nu}\alpha_{\lambda}}}$$ Consider how this expression behaves under a small variation of the metric and you obtain the result for $\delta n_{\mu}$.
Mar
31
comment Space-like Killing vector of Robertson-Walker metric?
Both of you are writing metrics on a portion of the full de Sitter spacetime. Four-dimensional de Sitter has topology $R^1 \times S^3$ and is conveniently realized as a hyperboloid in $R^5$. Various combinations of the coordinates on the hyperboloid give the metrics above, but will only cover part of the hyperboloid. There may be timelike Killing vectors on the patches associated with those metrics, but there is no global timelike Killing vector.
Feb
4
comment Treatment of boundary terms when applying the variational principle
The solution -- which goes back to the Regge and Teitelboim paper I mentioned -- is to add additional surface terms to the action until you have a functional that doesn't require $\delta g$ to fall off faster than whatever the appropriate asymptotics are. As long as the new surface terms are intrinsic to the boundary you can still impose Dirichlet boundary conditions. In AAdS spacetimes, the surface terms are the famous "boundary counterterms". The fundamental motivation for them is establishing a good variational formulation of the theory; finiteness of the action is a consequence of that.
Feb
4
comment Treatment of boundary terms when applying the variational principle
The problem isn't with GHY. It's the claim that adding GHY to the EH action leads to a "well-defined variational problem". Take the EH action and add the GHY term. The Schwarzschild solution should be a stationary point of this action, right? Now consider the change in the action due to a small variation of the metric. You will find that the surface terms in the first-order change in the action only vanish if $\delta g$ falls off faster than 1/r. You have an 'action' that allows Dirichlet boundary conditions, but it can't tell between Schwarzschild and other metrics with 1/r asymptotics.
Feb
4
comment Treatment of boundary terms when applying the variational principle
I'll let you know next time I head down, which will hopefully be soon.
Feb
2
comment Normalizable and non normalizable modes of gauge fields in AdS/CFT
Sorry -- I don't remember a reference off the top of my head. You can work this result out by first linearizing the Einstein equation (i.e., write the metric as $g_{\mu\nu} = \bar{g}_{\mu\nu} + h_{\mu\nu}$, where $\bar{g}_{\mu\nu}$ is the AdS metric and $h_{\mu\nu}$ is the graviton) and then solving for the leading z dependence of the graviton. Like I said before, this will be easier if you pick a convenient gauge for $h_{\mu\nu}$.
Feb
2
comment Normalizable and non normalizable modes of gauge fields in AdS/CFT
What I said above goes for the graviton, but you'll need to linearize the Einstein equation to get the equation of motion for the field. Choosing the right gauge will help simplify the intermediate steps of this calculation. You will eventually find that the equation of motion for the spin-2 graviton on the AdS background reduces to that of a massless scalar.