# Tag Info

16

I have never heard people talk about mathematical "consistency" of QFT in any other sense than that of rigor. Your mention of "Wightman axioms" supports this. This isn't about the mathematical notion of the consistency of logical system of axioms, it's about having a system of axioms and theorems in the first place and knowing how to ...

3

The renormalization applies to the parameters of the theory. Usually that means the masses, the charges (or coupling constants) and so on. That is, the parameters that you would measure to determine the theory. The usual way that happens is loop corrections. Mass gets measured. It correspoonds to a line in a Feynman diagram, and a propagator in the ...

3

It is not independent. To use your own example, consider the following regulator: $$\int_{m}^{\Lambda+1} dp\; p^2 = \frac{\Lambda^3}{3}+\Lambda^2+\Lambda - \frac{m^3}{3}+\frac13$$ whose finite part is $-m^3/3+1/3$ instead of just $-m^3/3$. So, what is the correct claim? The regulated version of the integral $$\int dp f(p)$$ can be thought of as a ...

2

Yes, the Slavnov–Taylor (ST) identities are generalized Ward identities for non-Abelian Yang-Mills theory with or without matter. (If there's matter the ST identities contain more terms.) More generally, any anomaly-free gauge theory can in principle be given a BRST formulation with corresponding generalized Ward identities.

1

You are right that a long calculation is not necessary. But I can also see how some introductions to renormalization would gloss over the physics of it, leaving people with the impression that it's merely some technical tool for Feynman diagrams. In this case, I would write your action with a bare mass S = \int_{\mathbb{R}^d}d^dx \left( \...

1

Disclaimer: Personally, I am not fully sure about this paper, since it outlines a connection between the Page curve and non-existence of global symmetries. For me, the idea of a Page curve in gravity is a bit difficult to digest since the Hilbert space of gravity doesn't factorize upon spatial partitioning due to the Gauss constraint. However the general ...

1

OP asks many questions. If we jump to OP's last question (which appears to be OP's real question), then the main point is that one cannot artificially exclude vertex interaction terms with less legs (such as, e.g. mass terms) unless they are prohibited by some symmetry. Even if they are absent in the UV, they get generated during the RG flow of integrating ...

1

In general, the Wetterich equation reads $$k \partial_k \Gamma_k = \frac{1}{2} {\rm Tr}\left[\left(\Gamma^{(2)}_k + R_k \right)^{-1} \cdot k \partial_k R_k \right],$$ where $\Gamma^{(2)}_k$ is a matrix of second-order derivatives of $\Gamma^{(2)}_k$ with respect to its arguments (here, $\phi$, $\psi$, and $\bar{\psi}$) and $R_k$ is the corresponding matrix ...

1

Like you said, we can include gravity perturbatively in the framework of low-energy effective QFT, as reviewed in reference 1. This works because gravity is extremely weak at the energies that characterize modern particle-physics experiments. But the interest in quantum gravity revolves around nonperturbative/high-energy/strong-field issues, like the ...

1

tldr: Neuberts statement is only true in massless EFTs when neglecting higher order contributions (i.e. Diagrams with two or more EFT vertices). As you found out, this statement of Neubert is in general incorrect. In fact it is not even really true for massless EFTs. In my opinion the setup of Operator renormalization is really rather confusing and opaque, ...

1

Gauge invariance protects the W and Z boson masses even without supersymmetry. The W and Z bosons are the massive gauge bosons from spontaneously broken electroweak symmetry. Consider the simpler case of an Abelian gauge symmetry. In this case, the symmetry acts on the gauge boson as a shift: $A_\mu(x) \to A_\mu(x) + \partial_\mu f(x)$ for some function \$f(x)...

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