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.

Filter by
Sorted by
Tagged with
1 vote
1 answer
19 views

Explicit derivation that the Faddeev-Popov functional determinant is gauge invariant

I am trying to show that the Faddeev-Popov functional determinant used in the quantisation of non-Abelian gauge theory is indeed gauge invariant. As shown in my previous question when we follow the ...
user avatar
1 vote
2 answers
83 views

Why is the determinant not integrated over in Faddeev-Popov?

In Peskin & Schroeder chapter 16.2 the authors go through the computation of the non-Abelian gauge boson propagator using the Faddeev-Popov procedure as is done for the QED case. The difference ...
user avatar
4 votes
0 answers
34 views

Form of the optical theorem in non-Abelian theory

I am studying chapter 16.3 from Peskin & Schroeder and I am trying to follow through the argument where we include contributions from ghosts to satisfy the Ward identity in non-Abelian gauge ...
user avatar
2 votes
1 answer
35 views

Showing that the integration measure is preserved under gauge transformation in the non-Abelian case

I am trying to show that the integration measure we use in the Fadeev-Popov method of quantisation of non-Abelian gauge theory is invariant under a gauge transformation. I am using Peskin & ...
user avatar
1 vote
1 answer
74 views

Does Yang-Mills have free gauge bosons?

Is there any physical problem with a propagating non-Abelian gauge boson? That is, a plane wave mode $A_\alpha^\mu e^{ikx}$, where $A_\alpha^\mu=b_\alpha\epsilon^\mu$, with $b_\alpha$ a constant ...
user avatar
1 vote
1 answer
59 views

Solution to Dirac equation with external source

The Dirac equation is: \begin{equation} \left[i\gamma^{\mu}(\partial_{\mu}-iA_{\mu})-m\right]\psi=0, \tag{1} \end{equation} where $A_\mu$ is a gauge field. The solution to this equation is:...
user avatar
  • 1,561
0 votes
1 answer
28 views

Sources to learn Gauge Theory, Groups, Lie Algebra, etc [duplicate]

As seen in previous questions, I'm interested in gauge theory, although I have no idea how to do any of the mathematics, though i'd like to start. With that in mind, Are there any good sources that ...
1 vote
0 answers
20 views

Why does expressing the Faddeev-Popov determinant as this lead to such problems?

Background In the following, I am interested in the Schwinger function associated with the gluon propagator when one considers the Gribov no-pole condition in the partition function. Defining $\nabla^{...
user avatar
1 vote
1 answer
46 views

Dirac propagator in Non-Abelian Theory

I am trying to derive equation (16.4) from chapter 16.1 page 506 of Peskin&Schroeder. Here is my derivation My Attempt We start here by considering the dirac spinor part of the Non-Abelian ...
user avatar
-2 votes
0 answers
28 views

What are the numerical values of the gauge coupling constants? [duplicate]

I mean the values of: $U(1)$ gauge coupling $SU(2)$ gauge coupling $SU(3)$ gauge coupling
user avatar
  • 11
0 votes
0 answers
36 views

Non-Abelian vertex 3-gauge-boson

I am trying to understand how the vertices depicted in page 507 of Peskin and Schroeder come about. I understand that vertex where we have 1 gauge boson and two fermions but I'm confused on the ...
user avatar
4 votes
3 answers
1k views

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 ...
user avatar
1 vote
1 answer
82 views

Yet more gauge group nonsense: $D3$? $Q8$? $Z8$?

This'll probably make me look like a total idgit, but I have a new question in the same vein as mine about $SU(4)$, but this time without any guesses. I've looked a bit into groups, and it looks like ...
user avatar
0 votes
0 answers
44 views

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.
user avatar
2 votes
1 answer
56 views

Vanishing of path integral over internal d.o.f. of test particle in $SU(N)$ gauge theory

In Ch-2 (Yang-Mills theory) of David Tong’s notes on gauge theory. Tong writes an action $$S_w=\int d\tau \hspace{2pt}i w^{\dagger} \frac{dw}{d\tau}+\lambda(w^{\dagger}w-k)+w^{\dagger}A(x^{\mu})w\tag{...
user avatar
  • 2,815
0 votes
0 answers
64 views

Noether current for self-dual Yang-Mills theory

The Lagrangian for self-dual Yang-Mills theory, in spinorial notations is given by $$\mathcal{L}= B^{a\, AB} (\partial_{A}{}^{A'} A^a_{A'B} + f^{abc} A^b_{A}{}^{A'} A^c_{A'B})$$ where $B^{a\,AB}$ is a ...
user avatar
0 votes
1 answer
138 views

What is the Mathematical description of Weak Interaction at low energies?

Introduction When I started to study gauge theory the mathematical road map seemed to be quite "simple". After all the concepts and notions about principal the differential geometry of fibre ...
user avatar
  • 2,679
0 votes
2 answers
74 views

$SU(2)$ comparator in Peskin & Schroeder

When Peskin and Schroeder build the comparator for a local $SU(2)$ (chapter 15.2), they say that near $U=\mathbb{I}$ any $2\times 2$ unitary matrix can be expanded in terms of the Hermitian generators ...
user avatar
  • 1,954
2 votes
1 answer
48 views

Problem in the general Einstein-Hilbert action of non-abelian Kaluza-Klein theory in four dimensions (1+1D, and 2D)

Background I am interested in the computation of the four-dimensional Einstein-Hilbert action seen as the "inverse" of the Kaluza-Klein procedure. That is, I want to write something like: \...
user avatar
1 vote
1 answer
106 views

Yang-Mills field-strength 2-form and exterior gauge-covariant derivative

I think that my problem is not having a formal definition of how the exterior covariant derivative works. What I know is that the exterior covariant derivative $D_A$ is defined as a generalization of ...
user avatar
  • 131
1 vote
0 answers
48 views

What is / why the fiber bundle connection one-form from a physics point of view?

Take the Yang-Mills gauge theory for example. Gauge field $A$ is the pullback of the connection one-form to the base manifold. Other concepts of gauge theory also find their definition in fiber ...
user avatar
  • 121
0 votes
0 answers
17 views

EMT in 2D Euclidean Yang Mills

In pure 2D Euclidean YM theory with $SO(8)$ gauge group. For Lagrangian $\frac{1}{4g^2} Tr(F_{\mu\nu}F^{\mu\nu})$ is energy momentum tensor $$T^{\mu\nu}=\frac{1}{g} Tr(-F^{\mu\rho}F_\rho^\nu+1/4\eta^{...
user avatar
  • 145
0 votes
1 answer
69 views

Identifying mesons with Goldstone modes

In QCD, due to the work of ‘t Hooft and Vafa-Witten, we know that confinement implies chiral symmetry breaking (David Tong’s gauge theory notes have a clear discussion of this). It is then said that ...
user avatar
  • 113
2 votes
0 answers
112 views

Why do we describe gauge fields by connections?

Let $\pi:P\rightarrow M$ denote a principal $G$-bundle, where $M$ is thought of as some spacetime and $G$ is an appropriate group (such as $\mathrm{U}(1)$ or $\mathrm{SU}(2)$). I want to understand ...
user avatar
  • 136
2 votes
0 answers
84 views

Commutation relations in quantised Yang-Mills

Consider Yang-Mills theory with gauge group $G$. Let $\{T^a\}$ be a basis for the Lie algebra $\mathfrak{g}$, so that the connection coefficients can be written as $A_\mu = A_\mu^aT^a$. In the ...
user avatar
3 votes
0 answers
63 views

Current conservation in Yang-Mills equations?

In electromagnetism, the equations of motion are \begin{align} dF &= 0 \\ *d*F &= J \end{align} From this, we can easily derive current conservation $d*J = 0$. The Yang-Mills equations appear ...
user avatar
  • 1,355
5 votes
0 answers
51 views

Initial value formulation of Yang-Mills equation

In Wald Chapter 10, he discusses the initial value formalism of electromagnetism - how Maxwell's equations are actually a system of three equations plus an initial value constraint, and how we can ...
user avatar
  • 1,355
-1 votes
2 answers
101 views

Intuitive meaning of Yang-Mills

Is it fair to say that the "new" thing about Yang-Mills equations is that they "bend" the probability amplitude locally like mass bends space in general relativity?
user avatar
  • 15
0 votes
0 answers
18 views

Reflection identity for color ordered gluon partial amplitudes

I'm currently studying various modern methods for calculating scattering amlpitudes, and I'm following Dixon's notes on the topic: https://arxiv.org/abs/hep-ph/9601359. When talking about the color ...
user avatar
  • 180
2 votes
1 answer
108 views

How does the BRST transformation act on ghost fields?

I understand the general idea behind constructing the BRST symmetry: take a generic gauge transformation $$\begin{equation} e^\omega, \end{equation}\tag{1}$$ where $\omega$ is Lie-algebra valued, and ...
user avatar
  • 21
1 vote
1 answer
52 views

Transformation of matter field in different representations in Yang Mills theory

I've read this post and also this one but I couldn't find my answer. My question is a stupid one. I know that matter fields in Yang mills theory can be transformed in any representation of gauge group,...
user avatar
0 votes
1 answer
68 views

Yang Mills Full Form Lagrangian

I am trying to derive the full form of the Yang-Mills Lagrangian(which should have been straightforward). I started from $$ L= -\frac{1}{4}F^{\mu\nu}_aF_{\mu\nu}^a $$ which gives $$ L = -\frac{1}{2}\...
user avatar
3 votes
1 answer
50 views

In lay terms, what are the real world consequence of the gauge invariances/symmetries upon which the Standard Model is built?

We learn that the SM is based on gauge invariance. Gauge invariance in turn is a consequence of symmetries (as I understand it) - meaning that a gauge theory having a symmetry is what makes it a gauge ...
user avatar
  • 4,087
2 votes
0 answers
61 views

Why is the Poisson bracket of the YM Hamiltonian with the secondary constraint zero?

Suppose we have the following Hamiltonian density $$\mathcal{H} = \frac{1}{2}\pi_i^a \pi_i^a + \frac{1}{4}F_{ij}^a F_{ij}^a $$ where $$F_{ij}^a = \partial_i A_j^a - \partial_j A_i^a + gf^{abc}A_i^b ...
user avatar
3 votes
1 answer
111 views

Expand an infinitesimal Wilson loop

I have a question about expanding an infinitesimal Wilson loop operator to get the field tensor $F_{\mu \nu}$ in chapter 3 of Fradkin's notes Classical Symmetries and Conservation Laws. For a ...
user avatar
  • 109
6 votes
1 answer
201 views

Isn't AdS/CFT an end to String theory as a fundamental theory?

I start with the Large $N$ QCD paper by 't Hooft. When 't Hooft published his paper on Large $N$ QCD it was clear why the string theory of hadrons due to Gabriele Veneziano could make sense. But at ...
user avatar
0 votes
0 answers
66 views

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 ...
user avatar
  • 3,294
1 vote
0 answers
40 views

Is there still a Gribov ambiguity when the Faddeev-Popov determinant is treated without ghosts?

In this document (Gribov Ambiguity by Thitipat Sainapha) the setup leading to the equation $3.77$ seems to strongly depend on the treatment of the Faddeev-Popov determinants with ghosts. Indeed the ...
user avatar
1 vote
0 answers
49 views

Dirac equation with an external Yang-Mills field

We know that the Dirac equation of a fermion coupled with a Yang-Mills field contains a term $i\gamma^{\mu}A_{\mu}\Psi$ describing this interaction (i.e. the interaction does not depend on the value ...
user avatar
  • 31
1 vote
1 answer
123 views

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 ...
user avatar
3 votes
1 answer
69 views

The residual gauge symmetry of Yang-Mills theory after Wick rotation

I am a bit puzzled by a statement in this question here. In particular, the claim that the residual gauge symmetry in Yang-Mills theory disappears upon Wick rotation to the Euclidean theory. For ...
user avatar
1 vote
0 answers
53 views

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 ...
user avatar
2 votes
1 answer
73 views

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)^...
user avatar
2 votes
0 answers
69 views

$Z_N$ one-form symmetry of $SU(N)$ super Yang-Mills

In Gaiotto's paper "Generalized Global Symmetry", a paragraph above (1.3) states a fact about the one-form symmetry of a gauge field: we start with a gauge theory based on a simply ...
user avatar
  • 497
0 votes
1 answer
110 views

Transformation of field strength tensor in non-abelian gauge theory

The field strength tensor is defined as $$F_{\mu\nu}^a=\partial_\mu A^a_\nu-\partial_\nu A^a_\mu +g f^{abc} A_\mu^b A_\nu^c$$ where $f^{abc}$ are the antisymmetric structure constants and $A_\mu^a$ ...
user avatar
5 votes
1 answer
158 views

Lagrangian for Gauge theory of gravity

There are a number of questions here discussing gravity as a gauge theory of the Lorentz group. I am trying to find the Lagrangian this gauge produces, and the other discussions stop just short of ...
user avatar
  • 1,372
1 vote
1 answer
70 views

Self-forces and backreaction in electromagnetic and gravitational forces

In classical electrodynamics is well-know the concept of self-force or self-interaction of any particle (much unlike two-body forces ruled by newton or coulomb forces!). What is the relation between ...
user avatar
  • 5,373
-1 votes
1 answer
77 views

What is the meaning of the Lie groups $ SU(3)\times SU(2)\times U(1)$?

In simple terminology, what is the meaning of $ SU(3)\times SU(2)\times U(1)$ ? What does it tell us about the standard model? Keep it mind I am still an undergraduate, the answer I am looking for isn'...
user avatar
  • 121
0 votes
0 answers
29 views

Gauge fixing of non-Abelian interactions [duplicate]

If we consider a non-Abelian potential $A_{\mu}=A^{a}_{\mu}T^{a}$ of a general non-Abelian group $G$, satisfying the property $F_{\mu\nu}=\partial_{\mu}A_{\nu}-\partial_{\nu}A_{\mu}+[A_{\mu},A_{\nu}]=...
user avatar
  • 31
1 vote
0 answers
49 views

Pure gauge of non-Abelian interactions [duplicate]

if we consider the $U(1)$ potential $A_{\mu}(x)=\partial_{\mu}f(x)$ (i.e. $F_{\mu\nu}=\partial_{\mu}A_{\nu}-\partial_{\nu}A_{\mu}=0$), then we can perform a $U(1)$ gauge transformation $A_{\mu} \...
user avatar
  • 31

1
2 3 4 5
12