Linked Questions
20 questions linked to/from Covariance in gauge theories: why should the Lagrangian be gauge invariant?
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Why insisting global invariance should hold locally? [duplicate]
In QED, when the Dirac Lagrangian is found to be not invariant under a local phase transformation,
$\psi$ $\longrightarrow$ $\psi'$ = $e^{i\theta(x)} \psi$
one tries to force it to get the desired ...
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What is the meaning of gauge theory and Yang-Mills theory? [duplicate]
I would appreciate it if you guys would help me to understand the idea behind these two concepts: Gauge field and Yang-Mills theory.
What I think I understand is: Suppose we have a Lagrangian that ...
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Why do we use local phase symmetry if we can couple the EM field to a divergence free current without it? [duplicate]
This question is pretty much what I am confused about. However, the answer says that we require local phase symmetry to keep the lagrangian gauge invariant. As far as I can see the argument only works ...
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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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Why is the $S_{z} =0$ state forbidden for photons?
If photons are spin-1 bosons, then doesn't quantum mechanics imply that the allowed values for the z-component of spin (in units of $\hbar$) are -1, 0, and 1?
Why then in practice do we only use the $...
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Why do we seek to preserve gauge symmetries after quantization?
Gauge symmetries do not give rise to conservation laws via Noether's theorem, and they represent redundancies in our description of the system. So why do we want to keep them after quantization? For ...
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Why do (can) we impose local gauge invariance?
Firstly, let me say that I understand that what basically happens in gauge theories is that we keep the unphysical degrees of freedom present but in check, instead of removing them at once, which ...
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What does it mean to be "gauging" a symmetry?
I read this and other similar questions, but they all address the problem of gauging a global symmetry (implying that one could also gauge a local one).
This confused me a lot: in my mind gauge and ...
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Global $U(1)$ transformation properties of gauge fields
What are the Global gauge transformations of gauge bosons in Standard Model?
To elaborate: Initially, we consider the global $U(1)$ transformations of scalars ($\phi$) and fermions ($\psi$) as
$$\...
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Is spacetime symmetry a gauge symmetry?
In previous questions of mine here and here it was established that Special Relativity, as a special case of General Relativity, can be considered as the theory of a (smooth) Lorentz manifold $(M,g)$ ...
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Is color charge quantized?
I was reading this stackexchange question, and found the answer to my question not totally answered. Clearly there is color and anti-color in analogy to electric charge, and color charge clearly ...
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Why do we require local gauge invariance?
My thought on this are somewhat scattered so I apologise in advance.
Maxwell's equations are gauge invariant. The physical Electric and Magnetic fields don't depend on whether we use $A_\mu$ or $A_\...
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Is the Bohm-Aharonov effect a proof of real $U(1)$ local gauge transformations "taking place" (instead of being just a math procedure)?
Under a local gauge (phase?) transformation of the field operator for electrically charged fields, $\psi \rightarrow e^{\mathrm{i}\phi(x_{\mu})}\psi$, where $e^{\mathrm{i}\phi(x_{\mu})} \in U(1)$, the ...
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Why does gauge invariance have physical consequences?
My understanding is that gauge invariance occurs when the description of a physical field as a mathematical field (i.e., function whose domain is space-time) contains a redundancy: there are ...
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What classifies gaugings?
Gauging a global symmetry $G$ introduces several free parameters to the theory. For example,
In $d=4$, gauging a simple and simply-connected Lie group introduces a coupling constant and a theta term, ...
