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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Energy Spectrum and Gauge Transformations

There is a question in SE about the fact that the Hamiltonian isn't invariant under the EM gauge transformations. I wanted to ask about its consequences here. I know that in general, the Hamiltonian ...
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Gauge Theory of Superconductors

I'm trying to understand better the nature of the gauge redundancy and the Higgs mechanism in superconductors. Specifically, I'm looking for a good reference that explains monopoles, vortices, and ...
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Is my proof of Proca Lagrangian local gauge invariance correct?

My task was to prove that the first term of the Proca Lagrangian is invariant under local gauge transformations. I’m new to Ricci calculus and think I’ve misinterpreted what I was supposed to do, and ...
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What, in simplest terms, is gauge invariance?

I am a mathematics student with a hobby interest in physics. This means that I've taken graduate courses in quantum dynamics and general relativity without the bulk of undergraduate physics courses ...
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Can we make the Dirac representation a gauge theory?

I'm looking for comments and references about an idea : gauging the Dirac representation of the Dirac matrices. What kind of field interaction would it give ? Specifically, the Dirac equation is ...
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Gauge transformation of vector potential multiplies wavefunction by phase

Consider an electron in an electromagnetic field with scalar and vector potentials $\phi, \mathbf{A}$. Suppose for simplicity that $\mathbf{A}$ is time independent. Suppose also that we know the ...
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From gauge invariance to charge conservation in covariant electrodynamics

I tried to solve the equations of motion using the action for the electromagnetic field interacting with a current, like $$L = F_{\mu\nu}F^{\mu\nu} + A_{\nu}j^{\nu}$$ getting the right Maxwell's ...
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How to apply the Faddeev-Popov method to a simple integral

Some time ago I was reviewing my knowledge on QFT and I came across the question of Faddeev-Popov ghosts. At the time I was studying thеse matters, I used the book of Faddeev and Slavnov, but the ...
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Gauge the symmetry $φ \to φ + a(x)$ for a free massless real scalar field

How does one alter the Lagrangian density for a real scalar field $$\frac{∂_μφ∂^μφ}{2}$$ such that is will be invariant under the gauge transformation $φ → φ + a(x)$? For a complex scalar field ...
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Why does a Gauge group have to be a compact Lie group? [duplicate]

In Topological Solitons by Nicholas Manton where he considers "compact Lie groups" to be the gauge groups for generalizing gauge theoretic concepts. But, he does not mention why that condition is ...
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What is the gauge field in Bose-Einstein condensation?

The Hamiltonian for bosons has $\phi^{\dagger}\phi$ terms in it which makes it U(1) invariant. Bose-Einstein Condensation apparently breaks such symmetry by choosing a definite phase, even though I ...
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When considering local phase transformations are we forced to use covariant derivatives?

When considering local phase transformations $e^{i\theta(x)}$ of the fields $\phi$ and $\phi^*$ corresponding to \mathcal{L}=\partial_\mu\phi^*\partial^\mu\phi-m^2\phi^*\phi \end{...
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How to find symmetry transformations?

For a given Lagrangian $${\cal L} = - \frac{1}{4} F_{\mu \nu} F^{\mu\nu} + |D_{\mu} \phi|^2 -V (\phi)$$ with $\phi = \frac{1}{\sqrt{2}} (\phi^1 + i \phi^2)$, there are the infinitesimal local ...
I am asked to find the gauge symmetry of the following Lagrangian: $L = -\frac{1}{4} F^2_{\mu \nu} + (\partial_{\mu} \phi_1 - m_1 A_{\mu})^2 + (\partial_{\mu} \phi_2 - m_2 A_{\mu})^2$ Then I have to ...