All Questions
Tagged with quantum-chromodynamics gauge-theory
77
questions
0
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47
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Is color charge internal symmetry or global symmetry?
I was told the color charge in the standard model could not be observed directly. This sounded like the gauge field $\vec A$ in the electromagnetism. However, it is a discrete charge and does have ...
- 3,256
0
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
answer
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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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
2
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0
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45
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QCD in Coulomb Gauge Kernel Expansion
I was re-reading the Hamiltonian QCD in Coulomb gauge section in Particle Physics and Introduction to Field Theory by T.D. Lee and I was trying to understand better the form of the Coulomb kernel that ...
- 45
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
1
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0
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35
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Question about semiclassical approach to QCD
I'm struggling to understand the usefulness of the semiclassical approach to QCD. In particular, by using this approach, we can analyze the vacuum structure of QCD, including theta-vacua, $n$-vacua, ...
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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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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
votes
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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78
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Color confinement vs. Weak charge confinement
Sometimes, color confinement is explained loosely by stating that the gauge group of QCD, namely SU(3), is non-abelian gauge group and, therefore, tends to form narrow "flux tubes" through ...
- 1,640
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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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0
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67
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$SU(N)$ gauge theory in black hole background
Assume you have standard $SU(N)$ gauge theory in a (non-asymptotically flat) black hole background (i.e., near the center of the black hole).
Given the extreme pressure and temperature, I assume that ...
- 2,188
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
9
votes
1
answer
1k
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What is confinement?
I just got confused about the meaning of confinement in QFT.
The naive definition is that in QCD one cannot observe isolated quarks and gluons. This is a trivial statement because in any gauge theory ...
1
vote
1
answer
320
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What are clover fermions?
I've seen the term been used quite a lot when reading about lattice gauge theory calculations. So far what I've gathered is the following, from this source [1].
Lorentz invariance of the action is ...
- 5,371
3
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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
views
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
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0
answers
233
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The heat bath algorithm for $SU(3)$ lattice gauge field
I'm studying lattice gauge theory and succeeded in simulating $U(1)$, $SU(2)$ with a heat bath algorithm. However, I have difficulty in applying the algorithm to $SU(3)$. I refer to Gattringer and ...
- 165
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83
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How does the electroweak interaction and QCD form $SU(2)$ and $SU(3)$?
I'm trying to get a foothold into quantum field theory from a mathematical background. I see the use of $SU(2)$ and $SU(3)$ in gauge theory and wonder the following questions to help me bring QFT ...
- 101
3
votes
2
answers
313
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Normalisation of QCD Lagrangian
In QCD, and more generally in representations of $\mathfrak{su}(N)$, there is a freedom to choose the normalisation of the generators,
$$
\mathrm{Tr} \, \left[R(T^a) R(T^b)\right] = T_R \delta^{ab}.\...
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2
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68
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Abelian theories with more than one charge
I have a question about the non-abelian character of QCD. In order to write a gauge-invariant Lagrangian, there must be a term with the strength tensor $X^{\mu\nu}_{a}X_{\mu\nu}^{a}$ where
$$
X^a_{\mu\...
0
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1
answer
108
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Can a gauge theory with $SU(2)_{left}*SU(2)_{additional}$ symmetry contain confinement?
Consider a gauge theory with $SU(2)_{left}*SU(2)_{additional}$ symmetry.
By $additional$, I mean adding a new symmetry between an electron and a quark(like up quark and electron forming a doublet).
...
- 1,268
5
votes
1
answer
430
views
How do $\theta$-terms not violate gauge invariance?
In the context of QCD (and more generally, any quantum gauge theory in even dimensions), the $\theta$-term is
$$
\frac{\theta}{8\pi^2}\langle F_A\wedge F_A\rangle = \frac{\theta}{32\pi^2}\langle F_A^{\...
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0
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237
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Polyakov loops and Wilson loops as order parameters
At zero temperature, the confinement/deconfinement criterion is the area/length law of the following non-local parameter called the Wilson loop:
\begin{eqnarray}
W=\text{Tr}\exp\left(\oint_CA_idx^i\...
- 813
5
votes
1
answer
1k
views
Color symmetry and flavor symmetry in QCD
In QCD, there is an SU(3) color symmetry for each flavor of quark as well as an SU(3) flavor symmetry for $u, d, s$ (although the latter is approximate). Why is there a gauge field for the SU(3) color ...
- 1,653
4
votes
1
answer
396
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What is the matrix form of the gluon field strength tensor?
For electromagnetism, the matrix form
$$\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
2
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0
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167
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QCD generating functional and QCD vacuum from nonperturbative to perturbative regime!
The complete generating functional in QCD (starting from the most general renormalizable, Lorentz invariant and gauge invariant Lagrangian) given by $$Z_\theta[J]=\int \mathcal{D}A \exp i\int d^4x~ {\...
- 26.8k
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2
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2k
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What's the difference between perturbative QCD, non-perturbative QCD, and gauge theory QCD?
I'm trying to get the ideal of QCD, and it turns out that there seems to be several versions, and some of which does not appear to agree with each other at a glance.
What's the difference, and how ...
- 3,256
3
votes
0
answers
58
views
Topological number and gauge invariance
In QCD or other non-abelian gauge theories, we come across infinitely many vacua that are gauge equivalent but have different topological numbers. We then say that the instanton solution is tunnelling ...
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1
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2
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424
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Why does QCD become strongly interacting at low energies and how low is low here?
A few days ago I asked a question about QCD chiral symmetry breaking and hopefully got a very good answer. But the problem is I am not well-versed in QCD to fully appreciate the answer there. I know ...
- 11.8k
2
votes
2
answers
573
views
Understanding the prefactor $\frac{\theta g^2}{32\pi^2}$ of the $F\tilde{F}$ term in Yang-Mills theories
The most general Yang-Mills (YM) action consistent with Lorentz invariance, gauge invariance and renormalizability should contain a term $$\kappa F_{\mu\nu a}\tilde{F}^{\mu\nu a}\tag{1}$$ where $\...
- 26.8k
1
vote
2
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746
views
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
3
votes
0
answers
324
views
A Question about Wave-Function Renormalization Factor in SQCD
Here, I have a question about the one-loop computation of the wave-function renormalization factor in SQCD.
According to Seiberg duality, the following electric $\mathrm{SQCD}_{e}$
\begin{gather}
...
- 2,923
2
votes
0
answers
72
views
What happens to large gauge transformations in gauges different from the temporal gauge?
There are already several questions regarding the meaning and definition of large gauge transformations.
Discussions of large gauge transformations typically only happen in the context of the ...
- 10.1k
2
votes
1
answer
529
views
$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)$ ...
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6
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0
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386
views
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
4
votes
1
answer
2k
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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
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203
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QCD vs. QED gauge invariance
Trying to understand the difference between QED and QCD gauge invariance treatment I found the following paper: https://arxiv.org/abs/1101.3425
I have the following questions:
I understand Eq. (42) ...
- 1,597
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$$
(Sum over $i$ implicit)
This Lagrangian ...
- 1,597
4
votes
1
answer
528
views
Is color charge quantized?
I was reading this stackexchange question, and found the answer to my question not totally answered. Clearly there is color and anti-color in analogy to electric charge, and color charge clearly ...
- 1,117
4
votes
0
answers
143
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What is the relation between the Gribov problem and color confinement?
I have heard that the Gribov problem is in some way related to color confinement (For instance: Gribov copies and confinement). Although I understand what both the Gribov and confinement problems are, ...
- 17.8k
3
votes
1
answer
267
views
Isn't there a unique vacuum of the Yang-Mills quantum theory?
The theta vacua$^1$ of a Yang-Mills quantum theory are given by $$|\theta\rangle=\sum\limits_{n=-\infty}^{\infty}e^{in\theta}|n\rangle.$$ In Srednicki's Quantum Field Theory, he claims that the ...
- 26.8k
6
votes
1
answer
2k
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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 ...
- 26.8k
1
vote
0
answers
75
views
Showing that $U(1)_R$ charge is non-anomalous in SUSY QCD when $r=\frac{F-N}{F}$
I'm trying to show that the value of the R-charge $r$ for which the R-symmetry is non-anomalous is given by $r=\frac{F-N}{F}$.
To do this we must calculate the triangle diagrams for the quarks $\...
- 4,780
3
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1
answer
171
views
What is the effect of including additional representations in the action of a lattice gauge theory?
I'm reading Introduction to Quantum Fields on a Lattice by Jan Smit. When introducing the lattice gauge-field action as a sum over plaquettes, Smit says that in general the action should include a sum ...
- 223
3
votes
0
answers
151
views
Which of the Wightman axioms are not incorporated by four dimensional quantum Yang-Mills?
I am trying to understand the quantum Yang-Mills existence problem but the best I have seen so far is the statement that there is no known interacting relativist field theory in four dimensions which ...
- 17.8k
4
votes
1
answer
159
views
QCD from chirally segregated, gauged $SU(3)_L \times SU(3)_R$?
There are already theory papers out there in which color $SU(3)_C$ is actually the diagonal subgroup of multiple $SU(3)$ factors. But due to a comment by @zooby, a new twist on this idea occurred to ...
- 13.1k
1
vote
0
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137
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Why is $SU(3)$ and not $U(3)$ the correct gauge symmetry? [duplicate]
If quarks come in three colours $r$, $g$ and $b$ than (neglecting all other quantum numbers and spacial freedom for now) a state of a quark would be a vector in $\mathbb{C}^3$.
If we are now looking ...
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