Recent content by Einj

All clear now! Thank you so much everyone!

Thanks a lot! Does that simply mean \sigma_8=\mathcal{P}(k=1/8 \,h/Mpc)? Where \mathcal{P} is the power spectrum.

Hi everyone, apologies if this question has been asked already. My search didn't give any results. Can anyone tell me the definition of \sigma_8 in terms of the power spectrum? A reference where I could find it is perfect too! Thanks a lot

Hello everyone, I am not an expert in the topic so I apologize in advance if the question has an easy answer. I think it is well known that if we have a set of N vortices in a superfluid their mutual interaction is logarithmic. Meaning that if \vec x_n is the position of the n-th vortex, then...

Hello everyone, I was wondering if anyone knows what the completeness relation for the fundamental representation of SO(N) is. For example, in the SU(N) we know that, if T^a_{ij} are the generators of the fundamental representation then we have the following relation $$...

Oh I see! Thanks a lot

Do you have any idea on how to show it or any source I could look at? Thanks for you reply!

Hello everyone, I have been reading around that when performing the analytic continuation to Euclidean space (t\to-i\tau) one also has to continue the gauge field (A_t\to iA_4) in order to keep the gauge group compact. I already knew that the gauge field had to be continued as well but I didn't...

Thanks for your reply. I indeed checked that for an action of the kind: $$ S=-\int d^4x\left(-(\partial_t+i\mu)\Phi^*(\partial_t-i\mu)\Phi +\vec\nabla\Phi^*\cdot\vec\nabla\Phi+m^2|\Phi|^2\right) $$ the 2-pt function in the Euculidean and Minkowskian case are related by an analytic continuation...

Thanks a lot for the quick answer! My question however, goes beyond lattice simulations. I don't have any lattice and everything is continuous. The questions is: is it still true that: $$ \langle O_1O_2\rangle (\tilde\omega,\vec k)\longrightarrow\langle T(O_1O_2)\rangle(\omega,\vec k) $$ when...

Hello everyone, my question is about Euclidean correlators (say a 2-pt function to be specific) in presence of non-zero chemical potential. The question in particular is: is it still true that the Minkowski time ordered 2-pt function can be simply obtained from the Euclidean one by analytic...

Hello everyone, I would like to know if there is a known, rigorous way to regularize a Green's function in coordinate space. In particular, it is known that the Green's function for a circle of radius R and source located at \vec x_0 is given by: $$ G(\vec x,\vec...

Thanks for the reply! How can non-gaussianity be generated at the level of inflation?

Hello everyone, I know this is a very basic question but I was wondering, in the context of inflation, what does it mean to have gaussian or non-gaussian fluctuations. First of all, are we talking about the fluctuations of the inflation? Second of all, how is the nature of the fluctuations...

Ok I will definitely do that! Thanks a lot.