All Questions
Tagged with renormalization yang-mills
44
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Asymptotic Freedom QCD
I'm trying to understand the derivation of asymptotic freedom with the renormalisation group equations. I'm reading Taizo Muta's book on QCD. What I don't understand is how he obtains the last ...
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Perturbative expansion and renormalization of non-abelian Yang-Mills theory solely in terms of gauge-invariant quantities?
In standard QFT, each term in the perturbative expansion for a gauge theory is not necessarily gauge-invariant. Only the whole sum of Feynman diagrams is guaranteed so.
However, at least for QED, ...
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Possible cases of matter fields for $SU(2)$ theory which retains asymptotic freedom?
Let us assume $4$ spacetime dimensions.
QCD, the $SU(3)$ gauge theory with quarks as the matter fields, have the asymptotic freedom property as long as there are 16 quark flavors of mass below the ...
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How does spin $j$ matter contribute to the running of the gauge coupling?
The one-loop beta function $\beta(g)$ for the gauge coupling $g$ with gauge group $G=SU(N_c)$, in a theory with $n_f$ spin-1/2 fermions in a representation $R_f$ of $G$, and $n_s$ complex scalars in a ...
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What happens to the Yang-Mills mass gap at high energies?
The mass-gap existence in quantum YM theory is the statement that the spectrum is bounded from below by some positive value $\delta$.
The spectrum should be independent of the energy at which you ...
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Does pure Yang-Mills have a scale?
Consider pure Yang-Mills (YM) in 4 dimensions. The YM mass gap problem (as described in https://www.claymath.org/wp-content/uploads/2022/06/yangmills.pdf) tells us that this is supposed to have a mass-...
- 742
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Renormalisation of Yang-Mills Breaks Gauge Invariance?
Consider the Lagrangian (renormalised + counterterm) of QED:
$$\mathcal{L} = -\frac{1}{4} F_{\mu \nu}F^{\mu \nu} - \frac{1}{2 \xi}(\partial_{\mu} A^{\mu})^2 + \bar{\psi}(i \displaystyle{\not} D - m)\...
- 1,778
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One-loop renormalization of the gauge coupling
Quoting Yuji Tachikawa, chapter 3 of "${\cal N}=2$ Supersymmetric Dynamics for Pedestrians":
Recall the one-loop renormalization of the gauge coupling in a general Lagrangian field theory $$...
user242231
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Fermion self-energy and vertex renormalization in Non-Abelian Gauge Theories
I am currently going through chapter 16 of Peskin and Schroeder and some of the calculations seem very obscure to me. The problems are as follows:
On page 528, the authors compute the value of the ...
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Can we make a massive non-abelian gauge field renormalizable by gauge fixing without Higgs mechanism?
There have been a lot of similar questions about this topic on this website, such as Gauge invariance is just a redundancy. Why is massive abelian gauge field renormalizable but massive non-abelian ...
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Beta function for $U(N)$ Yang-MIlls?
What is the one-loop beta function $\beta(g)$ for $U(N)$ pure Yang-Mills? I expect it to behave rather differently than $SU(N)$, since when $N=1$ we have electrodynamics, for which $\beta(e)=0$. As a ...
- 3,514
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1-loop diagrams in Scalar Yang-Mills
Disclaimer: I've been calculating the renormalization constants $Z_i$ for the ScalarQED seen as the abelian limit of the Scalar Yang-Mills, and I know that I've made some mistakes because I find the ...
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Does the Slavnov-Taylor identity still hold for scalar Yang-Mills?
I want to renormalize the minimally-coupled scalar Yang-Mills theory:
$$\mathcal{L}_{YM\phi}=(D_\mu\phi)^\dagger(D^\mu\phi)-\frac{1}{4}F_{\mu\nu}^a{F^{\mu\nu}}^a-\frac{1}{2\xi}(\partial_\mu {A^\mu}^a)^...
- 5,931
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What makes the (non-abelian) strong interaction so special that it leads to confinement?
The strong interaction has a coupling constant of $\alpha_s(91GeV)\approx 0.1$ whereas the weak interaction has a much lower coupling constant $\alpha_w \approx 10^{-6}$. Both theories are non-abelian ...
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The 1-loop anomalous dimension of massless quark field for $SU(N)$ gauge theory with $n_f$ quark flavours
Considering $SU(N)$ gauge theory with $n_f$ massless quarks
I want to find the anomalous dimension to order of 1-loop of the massless quark field, that defined by: $$\gamma_q(g^{(R)})=\frac{1}{2Z_q}\...
