A gauge theory has internal degrees of freedom that do not affect the foretold physical outcomes of the theory. The theory has a Lie group of *continuous symmetries* of these internal degrees of freedom, *i.e.* the predicted physics under any transformation in this group on the degrees of freedom. ...

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1answer
71 views

Is local chiral symmetry qualitatively the same as gauge symmetries?

I am confused by the role that local chiral symmetry plays in chiral perturbation theory. For the case of chiral QCD with three quark flavors, the Lagrangian is invariant under global ...
5
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1answer
158 views

Georgi-Glashow model and the VEV of the scalar field

Consider the Georgi-Glashow model, an $SU(2)$ gauge theory with a real scalar in the adjoint (thus a 3-vector in the colour space) $\phi$. The Lagrangian is $$ L = -\frac{1}{4g^2} F_{\mu \nu}^{\, a} ...
4
votes
1answer
419 views

Non-inertial frames in Lagrangian mechanics?

Building on this Phys.SE post I am interested in how non-inertial frames can be considered in Lagrangian mechanics. My understanding is that changing the reference frame causes a transformation of the ...
0
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1answer
97 views

How to write the Lagrangian in terms of a projection

We know that $$ L=\frac{1}{2}\left(\partial_{\mu} A_{\nu} \partial^{\mu} A^{\nu}-\partial_{\mu} A_{\nu} \partial^{\nu} A^{\mu}\right) $$ But how do we write the Lagrangian in the following way: ...
1
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1answer
59 views

Coupling an electric charge to a gauge field. How is it done in this setup?

In page 9 of Tachikawa's N=2 susy dynamics for pedestrians it says that an electric particle with charge $n$ in the first quantised setup (in what sense first quantised?), Wick rotated to Euclidean ...
1
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1answer
91 views

Dimensional reduction of SUSY theories

I know that if one reduces 10 dimensional $\mathcal{N}=1$ SYM theory to 4 dimensions one gets $\mathcal{N}=4$ SYM. There are other examples also. I have two related questions regarding this fact. ...
1
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1answer
166 views

Consequences of local and global anomaly

Are the physical consequences of anomalies associated with a local symmetry is different from that of a global symmetry? If yes, why? We have global anomaly in the standard model but not local ...
1
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1answer
96 views

Is EM interpreted in a principal or vector bundle?

I've read in a few places that EM is a $U(1)$-principal bundle; but is this correct? Isn't it rather an associated vector bundle using the adjoint representation of $U(1)$?
2
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0answers
80 views

Massive Gauge Bosons without Higgs Effect

In a possible theory like our Standard model but without a Higgs i.e.: $$ \mathcal{L}=i\bar{\Psi}_f\gamma_\mu D^\mu\Psi_f-\text{Tr}[G^b_{\mu\nu}G^{b\,\mu\nu}] $$ where $b,f$ run over the typical ...
2
votes
1answer
37 views

Gluon have colour-anticolour; what about weak bosons?

Gluons can be red-antiblue, or green-antired, etc. What about weak interaction bosons? (Say before symmetry breaking, to make matters simpler.) Is there a similar "weak charge" structure of ...
6
votes
2answers
74 views

How are quadruple gluon vertices related to $SU(2)$ and $SU(3)$?

I once read that the non-commutativity of the Lie Groups $SU(2)$ and $SU(3)$ is the reason that the weak and strong interactions have Feynman diagrams with quadruple vertices, where four gauge bosons ...
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2answers
415 views

How do gauge boson interact with elementary particles?

We know that gauge bosons are the force carriers of fundamental interactions, but how do the gauge bosons themselves interact with particles?
7
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1answer
239 views

Is Elitzur's theorem valid only in lattice field theory?

Elitzur's theorem, stating that spontaneous breakdown of a gauge symmetry is impossible, was originally proved for a lattice gauge theory. Is it valid in continuum field theory? Any ref?
2
votes
1answer
73 views

Are the pion fields in chiral perturbation theory complex or real fields?

The chiral perturbation theory Lagrangian is written $$\mathcal{L}_2=\frac{f_{\pi}^2}{4}Tr(D_{\mu}U^{\dagger}D^{\mu}U)$$ where $$U=e^{i\sqrt{2}\Phi/f}$$ and $$\Phi= \begin{pmatrix} ...
3
votes
1answer
86 views

Why must superpartners have the same gauge quantum numbers?

The title leaves it quite clear, why must superpartners have the same gauge quantum numbers?
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0answers
68 views

How does the Higgs field relate to the Yang-Mills fields and gauge theories in general?

I asked this in astronomy How does the Higgs field relate to the Yang-Mills fields and gauge theories in general? but they suggested I ask it here. It is very confusing. Is there an easy ...
2
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0answers
89 views

Mathematician learning theoretical physics [duplicate]

EDIT: I was aware of the supposed duplicate. But I'm interested in a clear and focused path through the basics to advanced theoretical physics such as string theory - a path that avoids studying ...
1
vote
1answer
74 views

Gauge freedom in tetrad

I asked the question in the MathOverflow, but didn't get any response. I thought maybe better luck here. I'm reading the following paper about Petrov type D space times called "Type D vacuum ...
1
vote
1answer
64 views

How to check if some term in the Lagrangian involving gauge bosons is gauge invariant without explicit computations?

Normally (for fermions and scalars) we can simply use the decomposition of tensor products of gauge group representations to find invariant terms that we can write into the Lagrangian. For example ...
0
votes
1answer
116 views

Do gauge bosons really transform according to the adjoint representation of the gauge group?

Its commonly said that gauge bosons transform according to the adjoint representation of the corresponding gauge group. For example, for $SU(2)$ the gauge bosons live in the adjoint $3$ dimensional ...
5
votes
3answers
574 views

Bianchi identity of a non-Abelian gauge theory?

How can one prove the Bianchi identity of a non-Abelian gauge theory? i.e. $$ \epsilon_{\mu \nu \lambda \sigma}(D_{\nu}F_{\lambda \sigma})^a=0 $$
7
votes
2answers
683 views

Vector Potential for Magnetic field when the field is not in simply-connected region

According to Poincare's Lemma, if $U\subset \mathbb{R}^n$ is a star-shaped set and if $\omega$ is a $k$-form defined in $U$ that is closed, then $\omega$ is exact, meaning that there's some ...
2
votes
1answer
161 views

Why is the electromagnetic four-potential $A_{\mu}$ not an observable?

Why within classical field-theory the electromagnetic four-potential (usually $A_{\mu}$) not an observable? In classical mechanics we don't have problems with energy measurements and in quantum ...
2
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0answers
71 views

AdS/CFT-duality: How does the $U(1)$ decouple form the $U(N)$?

A stack of N coincident D3-branes on its world-volume describe, at the lowest order in $\alpha'$ and in absence of non-trivial background fields, a supersymmetric $U(N)$ gauge theory as explained in ...
9
votes
2answers
502 views

Is electric charge truly conserved for bosonic matter?

Even before quantization, charged bosonic fields exhibit a certain "self-interaction". The body of this post demonstrates this fact, and the last paragraph asks the question. Notation/ Lagrangians ...
1
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1answer
95 views

Are all elementary interactions arising from a gauge theory?

The standard model of particle physics is based on the gauge group $U(1) \times SU(2) \times SU(3)$ and describes all well-known physical interactions but with exception that gravity isn't involved. ...
5
votes
1answer
137 views

Transformation Law for Covariant Derivative in $SU(2)$ Yang-Mills

In page 488 of Peskin and Schroeder, it is stated (emphasis mine): It is not difficult to check using (15.27) and (15.21) that, even for finite transformations, the covariant derivative has the ...
1
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1answer
46 views

Transformations of electroweak gauge field $W_\mu$ under $U(1)_{e.m.}$

As the vector boson field $W_\mu$ is, together with $Z^0$, the gauge field for the Standard electroweak model, I know it transforms as a connection under the $SU(2)\times U(1)_Y$ group. But, when this ...
0
votes
2answers
87 views

The notion of fixing a gauge

I don't understand the notion of gauge fixing; can we choose any gauge or are there some restrictions? For example why can we choose $\nabla\phi = 0$ here: Determine the Electric field using ...
4
votes
1answer
85 views

Why is $U(1)$ special when defining global charges?

For gauge groups like $SU(2)$ and $SU(3)$ etc. we know that observable states such as mesons or baryons must be charge neutral. However, for a $U(1)$ gauge group we can have charged initial states in ...
2
votes
1answer
70 views

Origin of integral of field strength tensor in path-ordered exponential in gauge field theory

When studying some gauge theories approach to problems in Mechanics, I've found the following integral $$P\exp\left[\oint A \ dt\right]=1+\dfrac{1}{2}\oint_{\partial ...
1
vote
0answers
91 views

Branes at the conifold

Consider $N$ $D3$-branes at the singularity of the conifold. This particular example can be viewed as a $AdS_{5} \times T^{1,1}$ in the near horizon limit, where the Einstein manifold has isometry ...
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votes
1answer
157 views

Are gauge theories always renormalizable?

Speaking of quantum field theories. Is one of the following implications correct? gauge theory (gauge invariant) => renormalizable renormalizable => gauge theory (gauge invariant) If yes do you ...
0
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0answers
56 views

Why gauge field should be vanishing on horizon?

When considering an AdS spacetime including a black hole, matter field and gauge field, the value of temporal component $A_t$ of the gauge potential $A_\mu$ on horizon always is set be zero, even the ...
3
votes
2answers
695 views

What is conformal gauge?

I often see in physics articles on gravity such notion as conformal gauge and Weyl transformation. They use Conformal gauge to change coordinates to transform metrics from arbitrary $$ds^2=g_{\mu ...
86
votes
5answers
10k views

Gauge symmetry is not a symmetry?

I have read before in one of Seiberg's articles something like, that gauge symmetry is not a symmetry but a redundancy in our description, by introducing fake degrees of freedom to facilitate ...
0
votes
0answers
328 views

Counting Degrees of Freedom in Field Theories

I'm somewhat unsure about how we go about counting degrees of freedom in CFT, and in QFT. Often people talk about field theories as having 'infinite degrees of freedom'. My understanding of this is ...
1
vote
0answers
38 views

Changing variables in a Lagrangian to obtain mass terms of gauge fields [closed]

Context: In a excercise, consider a SU(2) gauge theory. The Lagrangian of the theory contains the three gauge fields and some scalar matter fields: $\phi_1 , \phi_2$ form a SU(2) doublet (fundamental ...
4
votes
0answers
178 views

Geometric interpretation of quantum Yang-Mills field

In most books\articles review geometric interpretation of classical Yang-Mills field in terms of principal bundle, connections...etc. What are geometric interpretation of quantum Yang-Mills field? ...
2
votes
2answers
104 views
2
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0answers
80 views

Are mass terms forbidden in the Lagrangian because of parity violation or because fermions live in a complex representation?

Normally one argues that we can't write down Lorentz AND gauge invariant mass terms, because of parity violation, i.e. l-chiral and r-chiral fields transform differently. This means that mass terms ...
1
vote
0answers
52 views

Covariant derivative of Noether current [closed]

I am working with a non-abelian gauge gauge theory that has one gauge field and a complex scalar field. I am supposed to prove that \begin{equation} (D_\mu j^\mu)^a=0, \end{equation} where ...
12
votes
2answers
539 views

Why are non-Abelian gauge theories Lorentz invariant quantum mechanically?

I seem to be missing something regarding why Yang-Mills theories are Lorentz invariant quantum mechanically. Start by considering QED. If we just study the physics of a massless $U(1)$ gauge field ...
1
vote
2answers
351 views

Elliptic genus; What is it within string/M-theory?

What is the elliptic genus (see also Witten index) in string/M-theory and (susy gauge)field theory constructions out of them? What does it tell us heuristically and what is its relation to the ...
3
votes
0answers
302 views

Effective field theories and gauge anomalies cancellation

Lets assume some theory which concludes sets of generations of fermions (lets call them $A$ and $B$). Fermions $A$ have some gauge group $G_{A}$ (for example, SM), while fermions $B$ are charged under ...
1
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0answers
112 views

Is gauge invariance essential to a theory be renormalizable?

Let's consider a model of New Physics in which all operator have dimension smaller than four, but which breaks explicitly $SU(2)_L$ gauge symmetry. Is this model necessarily renormalizable? ...
1
vote
2answers
124 views

Why gauge fields are traceless Hermitian?

So I've had a read of this, and I'm still not convinced as to why gauge fields are traceless and Hermitian. I follow the article fine, it's just the section that says "don't worry about this ...
1
vote
1answer
195 views

Commutator of Gauge Covariant derivatives

What is the physical meaning of $$ [D_{\mu}, D_{\nu}] ~\propto~ F_{\mu, \nu}, $$ where $D_{\mu}$ is the gauge covariant derivative and $F_{\mu,\nu}$ is the field strength? Is it just a definition? ...
3
votes
1answer
115 views

Why is the gauge potential $A_{\mu}$ in the Lie algebra of the gauge group $G$?

If we have a general gauge group whose action is $$ \Phi(x) \rightarrow g(x)\Phi(x), $$ with $g\in G$. Then introducing the gauge covariant derivative $$ D_{\mu}\Phi(x) = ...
1
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0answers
32 views

Wu experiment and masses of neutrino

Wu experiment have shown that there are only left-handed neutrinos (and right-handed antineutrinos) take part in weak interactions. My question is about the significance of this experiment in a ...