All Questions
Tagged with quantum-chromodynamics yang-mills
93
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A list of failed attempts towards a proof of confinement [closed]
Can one give a list of failed or open attempts (not necessarily Supersymmetric) towards a proof of confinement in 4d regarding YM or QCD?
- 1,268
3
votes
0
answers
106
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The commutation relations of photon and gluon?
In QED, the photon field has the following commutation relations:
\begin{equation}
[A^{\mu}(t,\vec{x}),A^{\nu}(t,\vec{y})]=0, \tag{1}
\end{equation}
where $A^{\mu}(t,\vec{x})$ is the photon filed. ...
- 85
1
vote
1
answer
83
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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 ...
- 15
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votes
1
answer
59
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Visualization of a gauge field with non-null winding number
In QCD you may add the term $\mathcal{L}_{\theta} = \theta\dfrac{g^2}{16\pi^2} \text{Tr}F\tilde{F}$, which turns out to be a total derivative. Now, it can be proven that the action of this lagrangian ...
- 1,611
-2
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1
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68
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What makes electric and magnetic fields in Yang-Mills theories gauge co-variant?
Specifically in QCD, why is it so?
- 33
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Wilson loop is not an element of $\mathrm{SU}(3)$ in color deconfinement
The center symmetry in QCD comes from the
$$a\ \mathcal{P}\mathrm{exp}\left(ig_s \int_C dx^\mu \ A_\mu(x)\right) a^{-1} = \mathcal{P}\mathrm{exp}\left(ig_s \int_C dx^\mu \ A_\mu(x)\right),$$
where $C$ ...
- 87
-4
votes
1
answer
82
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Yang-Mills mass gap caused by gluonballs or because dark matter WIMPs?
Yang-Mills quantum field theory predicts the existence of the lightest massive Bosonic (i.e. integer spin) particle.
This massive Boson will be much lighter than the $W$ and $Z$ Boson and therefore ...
- 4,170
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0
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47
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How to derive the gauge invariance of Yang-Mills action with external source?
In the Faddeev-Popov procedure of path integral of
$$
Z[J] = \int [DA] e^{iS(A,J)},
\quad S(A,J)= \int d^4x [-\frac{1}{4}F^{a\mu\nu}F_{a\mu\nu} + J^{a\mu}A_{a\mu} ]
$$
we have used that $S(A,J)$ is ...
- 99
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2
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122
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Is there any physical reason behind the choice of Lie group in a Yang-Mills theory?
A Yang-Mills theory can be constructed for any Lie group that is compact and semisimple. The motivation behind this is discussed in this question. Is there any physical reason we choose $SU(3)$ or $U(...
- 3,350
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32
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Subleading correction to the gluon propagator in large $N$ expansion
I was reading Callan, Coote and Gross' paper on 2-dimensional QCD, where they show that the model that 't Hooft proposes in his work indeed produces quark confinement. In section VIII, they analyze ...
- 370
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1
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81
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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 ...
- 1,669
1
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0
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40
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Why is it justified to focus on gauge transformations constant at spatial infinity in QCD instantons?
In the context of Yang-Mills theories and QCD instantons, much of the literature and conventional treatment hinges on the consideration of gauge transformations that remain constant at spatial ...
- 841
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1
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267
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Why is there only one coupling constant in Yang-Mills theory? Why are gluon self-coupling and gluon-matter coupling constants the same?
Is it non-trivial that the coupling constant $g$ in gluon self-interaction terms is the same as the coupling constant $g$ in gluon-fermion interaction term in Yang-Mills theory?
Pure Yang-Mills theory ...
- 192
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1
answer
81
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Theta vacua eigenstates
I have been trying to prove the very simple result that the eigenstates of an operator with matrix elements
$$
\langle n^\prime | H | n \rangle \sim g(|n^\prime-n|),
$$
in a basis $\{|n\rangle\}^{+\...
- 1,742
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0
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244
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One-loop renormalization of the gauge coupling
Quoting Yuji Tachikawa, chapter 3 of "${\cal N}=2$ Supersymmetric Dynamics for Pedestrians":
Recall the one-loop renormalization of the gauge coupling in a general Lagrangian field theory $$...
user242231
3
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1
answer
59
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Can I switch the convention of QCD by replacing coupling constant $g$ with $-g$?
There are two equivalent conventions in QCD that give two different definitions of the covariant derivative operator: ${D_\mu } = {\partial _\mu } - {\rm{i}}gA_\mu ^\alpha {T_\alpha }$ and ${D_\mu } = ...
- 41
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votes
1
answer
968
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What is the physical meaning of the large $N$ expansion?
I know about the $1/N$ expansion for some time. Apart from the fact that as Witten suggests, it can be the correct expansion parameter of QCD Baryons in the $1/N$ Expansion (in a parallel that he ...
- 1,268
2
votes
0
answers
99
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Physical interpretation of the asymptotics of partition function in string theory
I would like to understand the physical interpretation of the asymptotic expansion of a partition function. The QCD partition function with gauge group $SU(N)$ as $N$ is large has been shown by Gross ...
- 121
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3
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1k
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Is the concept of bicolored gluons mathematically precise/meaningful? Please explain
Each flavour of quark carries a colour quantum number: red, green or blue. I know what it means mathematically. But elementary textbooks (e.g, particle physics by Griffiths) also say that gluons are ...
- 11.8k
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0
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107
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What would the force arising from an $SU(4)$ gauge field operate like? (As in, how many charges, whether the boson would interact with the force, etc)
Heyo, i'm new to this all, and deadly curious what this would look like. If this isn't specific enough, lemme know.
1
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506
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What does the Pontryagin index do in BPST instanton (solution to Yang-Mills theory)?
$$
\mathcal L = -\frac12\mathrm{Tr}\ F_{\mu\nu}F^{\mu\nu}+i\bar\psi\gamma^\mu D_\mu\psi
$$
We take this Lagrangian for QCD, after this I need to calculate BPST instanton with topological Pontryagin ...
3
votes
1
answer
258
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What makes the (non-abelian) strong interaction so special that it leads to confinement?
The strong interaction has a coupling constant of $\alpha_s(91GeV)\approx 0.1$ whereas the weak interaction has a much lower coupling constant $\alpha_w \approx 10^{-6}$. Both theories are non-abelian ...
- 9,778
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0
answers
124
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The 1-loop anomalous dimension of massless quark field for $SU(N)$ gauge theory with $n_f$ quark flavours
Considering $SU(N)$ gauge theory with $n_f$ massless quarks
I want to find the anomalous dimension to order of 1-loop of the massless quark field, that defined by: $$\gamma_q(g^{(R)})=\frac{1}{2Z_q}\...
12
votes
1
answer
1k
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How many colors really are there in QCD?
In abelian gauge theory (electrodynamics), the matter fields transform like (please correct me if I am wrong)
$$
|\psi\rangle\rightarrow e^{in\theta(x)}|\psi\rangle\tag{1}
$$
under a gauge ...
- 133
2
votes
2
answers
288
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Do the “$SU(3)$ colors” live in a 3-dimensional vector space?
Previously I asked a question about the visualized colors:
Do the "colors" live in a 3-dimensional vector space?
(My earlier question is unfortunately closed)
Now I like to ask the “$SU(3)$ ...
- 4,336
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0
answers
68
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Abelian theories with more than one charge
I have a question about the non-abelian character of QCD. In order to write a gauge-invariant Lagrangian, there must be a term with the strength tensor $X^{\mu\nu}_{a}X_{\mu\nu}^{a}$ where
$$
X^a_{\mu\...
-3
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3
answers
207
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Misunderstanding the dimension of QCD
From my point of view, the definition of the tension tensor is contradictory.
$$F_{\mu \nu}=\partial_{\mu} A_{\nu}-\partial_{\nu} A_{\mu} +ig[A_{\mu},A_{\nu}]$$
$$[A_{\mu}]=\frac{1}{cm \times g};[F_{\...
2
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0
answers
783
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QCD energy scale $\Lambda_{\rm MS} $, $\Lambda_{\rm QCD}$, ...?
Why there seems to be different conventions of QCD energy scales? Is that due to the running coupling?
For example in Wikipedia https://en.wikipedia.org/wiki/Coupling_constant#QCD_scale:
$$
\Lambda_{\...
- 4,336
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0
answers
237
views
Polyakov loops and Wilson loops as order parameters
At zero temperature, the confinement/deconfinement criterion is the area/length law of the following non-local parameter called the Wilson loop:
\begin{eqnarray}
W=\text{Tr}\exp\left(\oint_CA_idx^i\...
- 813
4
votes
1
answer
313
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Understanding the proof of the "Photon-Decoupling Identity" for colour-ordered Yang-Mills amplitudes
Problem:
To prove the Photon-Decoupling Identity for colour-ordered Yang-Mills amplitudes:
$$0= A(1,2,3,...,n)+A(2,1,3,...,n)+...+A(2,3,...,1,n) \tag{1}$$
I know I must use $(2)$, which expresses ...
- 753
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0
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31
views
Is tree-level QCD on-shell constructible, with BCFW?
Is tree-level QCD on-shell constructible, with BCFW?
Pure yang mills is on-shell constructible, what is one add into massless fermions?
- 1
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Equations of motion of classical chromodynamics with Yang-Mills theory
I am currently reading a paper about classical chromodynamics:
https://arxiv.org/abs/hep-th/0607203
However I have problems understanding equation (2) and (4)
(2):
\begin{equation}
F_{\mu \nu}= \...
- 1,219
1
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0
answers
64
views
Why is the self-energy for quarks in $d=2$ Large $N$ QCD only order $g^2$?
In an interesting article by 't Hooft , he is able to find the exact quark propagator, in the large $N$ limit of QCD. He finds that the full 1PI self-energy is given by:
$$\Gamma(p)=-\frac{g^2}{2\pi} \...
- 744
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votes
1
answer
396
views
What is the matrix form of the gluon field strength tensor?
For electromagnetism, the matrix form
$$\Bbb{F}^{\mu \nu}=\begin{pmatrix} 0 & E_x/c, & E_y/c & E_z /c \\ -E_x/c & 0 & B_z & -B_y \\ -E_y /c & -B_z & 0 & B_x \\ -...
- 1,548
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votes
2
answers
573
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Understanding the prefactor $\frac{\theta g^2}{32\pi^2}$ of the $F\tilde{F}$ term in Yang-Mills theories
The most general Yang-Mills (YM) action consistent with Lorentz invariance, gauge invariance and renormalizability should contain a term $$\kappa F_{\mu\nu a}\tilde{F}^{\mu\nu a}\tag{1}$$ where $\...
- 26.8k
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votes
1
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How can we tell a theory is confining?
Physically, I understand what it means for a theory to be confining. The elementary particles are not observable, but only composite particles are. The classic example is QCD, where quarks are ...
- 3,514
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288
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Intuition for Asymptotic Freedom
In QED, the $\beta$-function has a positive sign. This means that the coupling increases at higher energies, or equivalently, smaller length scales. This picture is made intuitively clear by the ...
user240990
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2
answers
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How does the underlying symmetry of QCD imply the allowance of a 4-gluon vertex?
Quantum chromodynamics allows for a four-gluon vertex such as this, in a diagram
Such a vertex would never be allowed in quantum electrodynamics, which has an underlying U(1) gauge symmetry.
I know ...
- 324
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1
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529
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$U(N)$ & $SU(N)$ : What's the conceptual difference in Gauge Theory?
I know the mathematical difference that one means $ absolutevalue(det) = 1$ and one means det = 1 (rotation) and that ones the subgroup of the other and so on.
But:
has a local/gauged $SU(3)$ ...
- 91
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1
answer
393
views
Are theta vacua topologically protected?
In discussions of Yang-Mills instantons it is often stated that one should sum in the path integral over all contributions of fluctuations around all the topologically distinct vacua labelled by ...
- 708
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386
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A Naive Question about Gauge Theory
I am suffering from a question I encountered from the lecture notes of gauge theory by David Tong. The problem comes from page 67 on the gauge fixing in back-ground gauge method. In David Tong's ...
- 2,923
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1
answer
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Why quarks in the fundamental and gluons in the adjoint?
I have been told that in gauge theories
“fermionic matter goes in the fundamental rep of $SU(N)$, while gauge fields go in the adjoint rep”.
I understand how this works, and for instance, in QCD,...
- 1,154
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562
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Wilson loop and Polyakov loop
As I understand, the Wilson line is the operator $W(x) = P\exp(i\int_{xi}^{xf} A.dx)$, where $P$ is path ordering. The Polyakov loop $P(x)$ on the other hand is the trace of the Wilson loop $W(x)$ ...
- 1,023
3
votes
2
answers
974
views
Invariance of Yang-Mills Lagrangian under charge conjugation
The Yang-Mills Lagrangian gauge invariant under an $SU(N)$ tranformation can be written as
$${\cal L} = -\frac{1}{4}F_{\mu\nu}^i F^{i\ \mu\nu} \tag1$$
(Sum over $i$ implicit)
This Lagrangian ...
- 1,597
4
votes
1
answer
528
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Is color charge quantized?
I was reading this stackexchange question, and found the answer to my question not totally answered. Clearly there is color and anti-color in analogy to electric charge, and color charge clearly ...
- 1,117
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votes
0
answers
696
views
Why is color confinement a difficult problem?
Assuming color force follows a constant rule of force instead of an inverse square rule of force. And that red, green and blue are all attracted to each other.
Why is color confinement considered a ...
user84158
4
votes
0
answers
143
views
What is the relation between the Gribov problem and color confinement?
I have heard that the Gribov problem is in some way related to color confinement (For instance: Gribov copies and confinement). Although I understand what both the Gribov and confinement problems are, ...
- 17.8k
3
votes
1
answer
267
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Isn't there a unique vacuum of the Yang-Mills quantum theory?
The theta vacua$^1$ of a Yang-Mills quantum theory are given by $$|\theta\rangle=\sum\limits_{n=-\infty}^{\infty}e^{in\theta}|n\rangle.$$ In Srednicki's Quantum Field Theory, he claims that the ...
- 26.8k
5
votes
1
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Covariant Derivative in QCD: How does it act on gluons?
Let the covariant derivative be $$D_\mu = \partial_\mu + \text ig\ A_\mu^a t^a,\quad a=1,\ldots,8$$where $g$ is the bare QCD coupling, $A_\mu^a$ are the eight gluon fields and $t^a=\tfrac{1}{2}\lambda^...
- 2,648
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1
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What is the Noether charge associated with the the color $SU(3)$ symmetry of QCD?
A version of the Noether's theorem applies to local gauge symmetries. What is the Noether's charge associated with a non-abelian gauge symmetry such as the color $SU(3)$ and how is that derived? I ...
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