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About equivalence of two ways of “derivation” of Standard model

Two ways of SM derivation I know two methods of SM lagrangian "derivation". The first one, which I will call as Weinberg way, is based on approaches of SM as theory with spontaneusly broken ...
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1answer
19 views

Vector potential in gauge transformation

While applying Gauge transformation, $\psi\prime = U \psi$ , where $ U= e^{i q \lambda(x)}$ , transformation law for "Vector Potential" comes out to be : $$ A_{\mu}\prime= ...
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1answer
48 views

$U(1)$ local gauge invariance in QED [duplicate]

While constructing Lagrangian of QED, we don't add the mass term for photon $\dfrac{1}{2} m^{2}A_{\mu}A^{\mu}$ because gauge invariance does not allow. I want to ask, whether "$\bf{Theoretically}$", ...
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0answers
25 views

Local Gauge Invariance and Masslessness [duplicate]

I am wondering if the masslessness of photons is due to the local gauge invariance of $u(1)$-gauge fields. The reason why I consider about this question is that I remember that the Proca field is not ...
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0answers
29 views

Noether Charge and Gauge Fields

I understand the global gauge symmetry results conserved charges associated with the symmetry. My question is, why don't we have conserved charges associated with local gauge symmetry of the gauge ...
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41 views

Noether's 2nd Theorem and Local Gauge Identities

I am trying to derive the so called Gauge Identities: \begin{equation} D_\nu\frac{\delta S}{\delta\phi} = 0 \end{equation} Where $D_\nu$ is an operator involving derivatives and $\frac{\delta ...
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1answer
68 views

Canonical spinors from gauge transformations

In this 2006 paper, http://arxiv.org/abs/hep-th/0610128, there is the concept of gauge transformation and how was it employed that I do not fully understand. Note, what will be talked about below is ...
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0answers
39 views

Physical proceses before the breaking of $SU(2)_L\times U(1)_Y$ symmetry

The energy scale which the electromagnetic and the weak interaction were unified, there were 4 massless gauge bosons: 3 corresponding to the unbroken generators of $SU(2)_L$, say $W_{\mu}^{1,2,3}$ ...
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29 views

global transformations in 3d gravity

I am currently working on proper and improper gauge transformations in 3d gravity and btz black holes. (because I have seen it defined with many different ways I will just say that with "proper"and ...
2
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0answers
58 views

(Super)Gauge Fixing in Supersymmetry

I have three questions about gauge fixing in supersymmetry, one is general and the other two explicit: Why gauge fixing seems not important in supersymmetry? By "not important" I mean gauge fixing ...
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1answer
59 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 ...
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1answer
40 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 ...
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1answer
90 views

What happens to theoretical physics if a photon has non-zero mass?

I want to know the theoretical implication if photons have a non-zero mass. What happens to the Maxwell equations? What happens to QFT? If the photon have mass it can decade?
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0answers
43 views

Gauge invariance of classical XY spin model

I am trying to understand gauge invariance as it is applied to a XY model Any ideas if it is in fact gauge invariant? Examples of how it is or isn't would be very helpful. If it is not gauge ...
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1answer
67 views

Phase on Aharonov-Bohm effect doubts

How I show that $$\Lambda(\textbf{x}')=\frac{q}{\hbar}\int \mathbf{A} \cdot d\mathbf{x'}$$ on $$ \tilde{\psi}(\textbf{x}',t)=e^{[\frac{iq\Lambda(\textbf{x}')}{\hbar c}]}\psi(\textbf{x}',t)$$ for ...
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177 views

What role does “spontaneously symmetry breaking” played in the “Higgs Mechanism”?

In talking about Higgs mechanism, the first part is always some introduction to the concept of spontaneously symmetry breaking (SSB), some people saying that Higgs mechanism is the results of SSB of ...
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1answer
67 views

What is a “local” lorentz transformation of vielbein? How does it transform?

I'm struggling with Anthony Zee's chapter on differential forms in Einstein Gravity in a Nutshell, page 600. He asks us to prove that $$\omega= \Lambda \omega' \Lambda^{-1} - (d\Lambda) \Lambda^{-1}$$ ...
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1answer
105 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 ...
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2answers
65 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 ...
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1answer
64 views

Photon emission/absorption by an atom and local gauge invariance

I understand that the local gauge invariance leads to a photon emission/absorption when the phase of an electron field is changed while the amplitude being unchanged. I'd like to know whether this ...
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1answer
93 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 ...
2
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1answer
119 views

Does Conformal Invariance of the Polyakov Action in Conformal Gauge imply Conformal Invariance of the Pre-gauge-fixed Polyakov Action?

In bosonic string theory the Polyakov action can be put in into conformal gauge. It is then possible to show that the resulting gauge fixed action is conformally invariant. Actually it's shown that ...
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0answers
37 views

Does fixing a metric component have anything to do with diffeomorphism invariance?

It is well known that in general relativity, the metrics $g_{\mu \nu}$ and $g_{\mu \nu} + \epsilon L_\xi g_{\mu \nu}$ are physically equivalent, where $L_\xi g_{\mu \nu}$ is the Lie derivative of the ...
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0answers
44 views

Are hilbert spaces invariant under gauge transformations?

I'm trying to work out if the physical hilbert space is invariant under any gauge transformation? I have found situations where under some transformations they don't change but I've now gotten very ...
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1answer
84 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? ...
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1answer
35 views

Higgs mass and EW precision tests

I'm trying to understand how the Higgs mass can influence EW precision tests. In order to do that I'm using the following document (section 4.3): http://arxiv.org/pdf/0706.0684v1.pdf There are a ...
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1answer
81 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) = ...
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2answers
150 views

What are global and local gauge invariance defined as they are?

I'm sorry for the triviality of my questions. Why is $\bar{\psi} = e^{i \theta}\bar{\psi}$, where $\theta$ is a real number, used as the global gauge transformation? Why $e^{i \theta}$; what's the ...
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0answers
40 views

A question on Gauge fields [duplicate]

Gauge fields play an important role in describing forces. It is very important in Lagrangian mechanics to derive the laws of motion of different systems. The laws of motion doesn't depend on gauge ...
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2answers
109 views

Time dependent Hamiltonian and Gauge invariance

In general, in quantum mechanics we can prove probability current or the Schrodinger equation and other quantities are gauge invariant. However, the Hamiltonian isn't gauge invariant. Under a gauge ...
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0answers
72 views

Argument of E. Fradkin on the mean-field theory of spin liquids

I have read the chapter 8 of Field Theory of Condensed Matter Physics (2ed.) by E. Fradkin a couple of times, but I still confused by his argument at some points. I hope you can help me with that. ...
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2answers
98 views

Gauge transformation of Lagrangian

Suppose I have a Lagrangian density $\mathcal{L}(\phi^\mu,\sigma)$ depending on vector fields $\phi^\mu$ and their derivatives and a scalar field $\sigma$ and its derivatives. If I make a gauge ...
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1answer
109 views

Why is tree-level interaction between neutral scalar and photons non-renormalizable?

I've read that the decay of a neutral scalar particle into two photons, i.e., $$ S(p+q) \to \gamma(p) + \gamma(q) $$ can't happen via tree diagrams and instead is caused by loop diagrams (such as a ...
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1answer
52 views

Does a Static E-field Increase the Gauge Invariant Vector Potential Without Bound?

The gauge invariant formulation of Maxwell's Laws (7.13): Indicates that the transverse electric field is the time derivative of the transverse vector potential. This gauge invariant vector ...
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1answer
100 views

Question on boundary condition for Maxwell's Equations and Coulomb's law

When deriving Coulomb's law using the differential forms of Maxwell's equation, the boundary condition that $\phi = 0 $ at infinity is also used. From $\nabla × E = 0, E = \nabla \phi$ for some ...
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2answers
232 views

Electric current $j^{\mu}$ in standard QED vs. scalar QED

The expression for the 4-current $j^{\mu}$ in standard QED is $$ e\bar{\Psi}\gamma^\mu\Psi $$ and $$ \frac{e}{2 i}(\psi^\dagger D^\mu \psi - (D^\mu \psi)^\dagger \psi) $$ in scalar QED. I ...
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1answer
114 views

Gauge invariance (QED)

In his book, the author says that according to the Feynman diagrams of this process in QED $$e^+ e^- \rightarrow \gamma \gamma,$$ gauge invariance requires that $$k_{1\nu}(A^{\mu\nu} + ...
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0answers
40 views

Gauge invariance and non-commuting second derivatives

I'm currently doing a homework assignment in relativistic quantum mechanics, and one of the problems involves proving the gauge invariance of a particular lagrangian. The problem is really quite ...
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2answers
58 views

Is a constant transformation still considered a gauge transformation?

I've never even considered the possibility that a constant transformation would not qualify as a gauge transformation. But I'm reading a paper that seems to make exactly this distinction. In ...
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0answers
66 views

Why are gauge symmetries continuous?

All gauge theories that are considered in literature are continuous $SU(N)$ symmetric. My question is why are always continuous groups considered for gauge symmetries? Why don't we consider discrete ...
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2answers
191 views

Wess-Zumino Gauge in non-Abelian supersymmetric theory

I've got a question concerning non-Abelian supersymmetric gauge theories. Consider supersymmetric non-Abelian theory realized on chiral superfields $\Phi_i$ in a representation $R$ with matrix ...
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1answer
70 views

In what sense are photons emergent?

Recently I read in an essay by Wilczek: "Photons are mixtures of weak B3 and hypercharge C mesons. It is those objects, not the emergent photon, whose properties are ideally simple." Until now I ...
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0answers
114 views

How can gauge invariance be unphysical?

Gauge symmetry is said to be "unphysical" because the transformations - unlike changes of reference frame - do not correspond to real physical operations. But the consequences of gauge symmetries are ...
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1answer
57 views

In which contexts are gauge theories applied?

According to the book Quantum Field Theory for the Gifted Amateur, on page 128 they say A theory which had a field $A^\mu(x)$ introduced to produce an invariance with respect to local ...
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0answers
32 views

Can any global symmetry be promoted to the local symmetry? [duplicate]

Can any global symmetry be promoted to the local symmetry? Does there exist counterexample?
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1answer
163 views

Free Electromagnetic field in Lorenz gauge

To get rid of the extra term in the QED Lagrangian we need to redefine the electromagnetic four-vector: $A^{\mu} \rightarrow A^{\mu} - \frac{1}{c} \partial_{\mu} a(x)$ where $a(x)$ is the function ...
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2answers
175 views

Classical EM : clear link between gauge symmetry and charge conservation

In the case of classical field theory, Noether's theorem ensures that for a given action $$S=\int \mathrm{d}^dx\,\mathcal{L}(\phi_\mu,\partial_\nu\phi_\mu,x^i)$$ that stays invariant under the ...
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0answers
65 views

Gauge invariance of Fermi's golden rule

I am having some issues with gauge invariance of Fermi's golden rule. Say we have a system Hamiltonian for a particle in an electric field and some additional potential $V$ with ...
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1answer
63 views

How one can know the gauge field emerging from the local gauge invariance is actually the EM field? [closed]

How one can know the gauge field emerging from the local gauge invariance is actually the EM field? I understood in a simple scalar field whose Lagrangian is given by $ \mathcal{L} = ...
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0answers
26 views

Understanding better this physical phrase [duplicate]

In field theory, symmetry governs the dynamics by restricting the form of the Lagrangian from which all relevant equations and interactions are derived. An example of symmetry transformations is ...