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Short version: LIGO matches their data onto waveforms calculated in numerical relativity. The mathematical study of black hole solutions plays a significant role in this; we couldn't trust our infer …

Other people have said that the problem is that GR isn't renormalizable. I want to explain what that means in measure-theoretic terms. What I say won't be 100% rigorous, but it should get the general …

I think a lot of the trouble people are having with this question comes from the phrase 'applications of quantum field theory'. Quantum field theory is a collection of ideas under active development …

The term "Yang-Mills theory" in the mass gap problem refers to a particular QFT. It is believed that this QFT (meaning its Hilbert space of states and its observable operators) should be defined in t …

What reasons are there for describing the harmonic oscillator as being so important in physics? The harmonic oscillator tends to show up when you're expanding a potential function around non-degenera …

CQFT is very much still an open research subject. I don't think it is known what the best approach is. So all I can do is share my own opinion. (And a warning: I'm just an interested observer!) Fir …

I think it might be worth pointing out that there are two kinds of topological quantum field theory, (Albert) Schwarz-type theories and Witten-type theories. In Schwarz type theories (like Chern-Simo …

I keep seeing this question percolate up. I think it deserves at least one more or less correct answer. First, the 1d integrals $I(a,b) = \int_{\mathbb{R}} \exp(-\frac{1}{2}x^2 - ax - b x^4) dx$ ce …

You ask 'why spectral theory instead of rigged Hilbert spaces?'. There are some practical/pedagogical reasons: One is that you'll need basic spectral theory in quantum mechanics anyways, so might as …

I can give individual answers to a lot of your questions, but I can't answer any of them completely, nor can I fit all these answers together into a coherent whole. For string theory, there does seem …

Sebastian points out correctly that $D$ and $d+d^{\dagger}$ are not the same objects. $D$ acts on spinors; $d + d^{\dagger}$ acts on differential forms. Physicists do sometimes make use of a trick …

You've got the right concepts, but they're presented in a way that makes me think some context could be helpful. In #1, you're really talking about the special case where $V$ is one of the spinor repr …

I am not sure if this is an answer or a request for clarification. There are a lot of different topics in math (and in physics) that go by the name 'topological quantum field theory'. Beyond the init …

It sounds like what you would like is a rigorous version of Witten's original Feynman integral & Wilson loop approach. This is not a totally unreasonable thing to ask for, since QFTs have been rigoro …

So, you must be talking about quantum field theories, as mass is something we associated with particles, which are a quantum phenomenon in field theories. In QFT, there are operators which create par …