Questions tagged [yang-mills]
Yang–Mills theory is a QFT, a *gauge theory* normally symmetric under a compact non-Abelian Lie group relying on (originally massless) gauge vector fields. YM theories describe the strong and electroweak interactions of elementary particle physics, the Standard Model.
9
questions
0
votes
0
answers
56
views
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
0
votes
1
answer
99
views
How to expand $(D_\mu\Phi)^\dagger(D^\mu\Phi)$ in $SU(2)$?
I would like to calculate the following expression:
$$(D_\mu\Phi)^\dagger(D^\mu\Phi)$$ where $$D_\mu\Phi = (\partial_\mu-\frac{ig}{2}\tau^aA_\mu^a)\Phi$$ and $A_\mu^a$ are the components of a real $SU(...
- 43
0
votes
1
answer
74
views
Gauge transformation rule for $dA$, where $A$ is the gauge field
Let $G$ be a non-Abelian simple compact gauge group and $\{ t^\alpha\}$ be a normalized set of generators for its Lie algebra $\mathfrak{g}$. Let $C^{\alpha \beta}_\gamma$ be the coupling constant for ...
- 1,669
0
votes
2
answers
59
views
Writing gauge transformation of the gauge fields explicitly in terms of coordinates
Let $G$ be a non-Abelian simple compact gauge group and $\{ t^\alpha\}$ be a normalized set of generators for its Lie algebra $\mathfrak{g}$. Let $C^{\alpha \beta}_\gamma$ be the coupling constant for ...
- 1,669
2
votes
1
answer
92
views
Is tetrad postualte independent of gauge field?
Here is what I know, $g_{\mu \nu} = e^{a}_{\mu} e^{b}_{\nu} \eta_{ab}$ and the tetrad postulate is
\begin{equation}
D_{\rho} e^{a}_{\nu} = \partial_{\rho} e^{a}_{\mu} - \Gamma^{\lambda}_{\rho \nu}e^{a}...
- 41
1
vote
0
answers
35
views
Derivation of the Noether current (Gauss law operator) in anomalous chiral gauge theory
I am reading Fujikawa-Suzuki's Path Integrals and Quantum Anomalies, §6.3. The Lagrangian I am looking at is
\begin{equation}
\mathcal{L}=-\frac{1}{4g^2}\left(\partial_\mu L_\nu^a-\partial_{\nu}L_\mu^...
- 29
0
votes
0
answers
31
views
Why the Slavnov operator is self-adjoint? [duplicate]
In the context of BRST we can define the Slavnov operator $\Delta_{BRST}$ which generates BRST transformations. My lecture notes claim that $\Delta_{BRST}$ is self-adjoint, but I don't see why.
- 357
3
votes
0
answers
106
views
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
0
votes
3
answers
222
views
2+1-dimensional $SU(N)$ Yang-Mills Theory
In recent years, there has been significant progress and growing interest in conducting quantum simulations of field theories using quantum devices. This typically involves formulating a Hamiltonian ...
- 857