Recent content by leo.

There is an important point about Eq. (4) in the OP that I forgot to mention when starting the thread, which is the definition of the ##f(\bar{\theta},\theta)## map appearing in Eq. (5) when defining the matrix ##h^a_{\phantom{a}b}(\theta)##. It is the coordinate representation of the group...

This seems to be what Robert Ticciati does on the book "QFT for Mathematicians". If I understand, given the Lie algebra representation ##D : \mathfrak{g}\to \mathfrak{gl}({\cal H})## he tentatively defines ##U:G\to GL({\cal H})## to be $$U(\exp tX) = \exp tD(X),\tag{1}$$ on which the ##\exp## on...

In Quantum Mechanics, by Wigner's theorem, a symmetry can be represented either by a unitary linear or antiunitary antilinear operator on the Hilbert space of states ##\cal H##. If ##G## is then a Lie group of symmetries, for each ##T\in G## we have some ##U(T)## acting on the Hilbert space and...

This is one problem from Robin Ticciati's Quantum Field Theory for Mathematicians essentially asking us to find Cartan subalgebras for the matrix algebras ##\mathfrak{u}(n), \mathfrak{su}(n),\mathfrak{so}(n)## and ##\mathfrak{so}(1,3)##. The only thing he gives is the definition of a Cartan...

I'm trying to learn about Abstract Wiener Spaces and Gaussian Measures in a general context. For that I'm reading the paper Abstract Wiener Spaces by Leonard Gross, which seems to be where these things were first presented. Now, I'm having a hard time to grasp the idea/motivation behind the...

I did that. The one I have already spoken to seems to be the only available advisor in the moment which has interest in QFT/gravity in the department. He asked me to come up with something concrete, however, so he asked for suggestion of some objective. One remark is that on that department...

I have a major in Mathematics and Mathematical Physics and I'm finishing a masters in Physics (just finishing to write down the dissertation really). I have also already enrolled the PhD course so that I need now to pick an advisor and a theme before june. My main interest since the early days...

That's exactly my problem. I don't know how to define the S matrix. It may really be the problem that this doesn't fit scattering theory at all, although I have one impression that it can be seen as scattering. In Hawking's papers for instance, one considers ##\mathcal{I}^-## to be one "initial...

Yes, the "Particle Creation by Black Holes" as well as some other references like Parker's QFT in Curved Spacetimes book. But all of them seem to discuss a different matter: how one observer at ##\mathcal{I}^+## perceives the natural vacuum for an observer at ##\mathcal{I}^-##. This is answered...

Here we consider a black hole formed by gravitational collapse classically. We also consider a scalar massless Klein-Gordon field propagating on this background. To quantize the field we expand it in appropriate modes. The three sets of modes required are: The incoming modes, appropriate for...

So in the end, ##\psi(t,\mathbf{x})## can be seen as the free evolution - with the Klein-Gordon equation - of a single particle in the initial state ##\psi(0,\mathbf{x})## as one would do with relativistic quantum mechanics without fields? As you say this has a few interpretational problems...

Let us consider QFT in Minkowski spacetime. Let ##\phi## be a Klein-Gordon field with mass ##m##. One way to construct the Hilbert space of this theory is to consider ##L^2(\Omega_m^+,d^3\mathbf{p}/p^0)## where ##\Omega_m^+## is the positive mass shell. This comes from the requirement that there...

I have taken one first QFT course last year which used Matthew Schwartz "Quantum Field Theory and the Standard Model" book. The course went all the way to renormalization of QED, although path integrals weren't discussed. Now I want to continue learning QFT and also I want to make a second...

@martinbn I thought the same when I've read section 2 of Sachs' paper the first time. But notice that Strominger points out that any geometry can be locally written in these coordinates with that metric tensor. I actually have the impression that it is true. My problem is that if any geometry...

I'm trying to understand the BMS formalism in General Relativity and I'm in doubt with the so-called Bondi Coordinates. In the paper Lectures on the Infrared Structure of Gravity and Gauge Theories Andrew Strominger points out in section 5.1 the following: In the previous sections, flat...