# Tagged Questions

Invariance of a physical system (its action) under a continuous group of local transformations underlain by a global symmetry whose group parameters fixed in space-time have now been extended to vary in space-time instead. Use for buildup of the invariance, fixing the gauge, and accounting for the ...

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### Three gauge bosons vertex

I was told that two $Z$ bosons could not decay to one (virtual) $Z$ boson at any loop level. Is it true? if so, why? Does it also hold for photons? Could we generalise the statement to "There cannot ...
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### How can spin be gauge dependent?

Deriving the spin (density) of an electromagnetic wave, I obtained the formula $$\mathbf S = \mathbf E \times \mathbf A$$ But under a gauge transformation $\mathbf A+\nabla f$ this function seems to ...
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### Yang and Mills' (and others') justification for local gauge invariance

In most physics textbooks, local gauge invariance is simply postulated---you start with a global symmetry, e.g. the global phase, then allow it to depend on the spacetime point, make the necessary ...
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### 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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### 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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### 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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### 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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### 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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### 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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### 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 $V$...
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### 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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### 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} + \tilde{A}^{\...
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### 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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### 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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### 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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### 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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### 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 ...
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 ...