Questions tagged [gauge-theory]
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. Examples include the $U(1)$-symmetric quantum electrodynamics and other Yang-Mills theories wherein non-Abelian groups replace the $U(1)$ gauge group of QED.
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Understanding the Gaussian weight and the parameter $\xi$ when quantizing gauge theories
In section 9.4 of Peskin & Schroeder's textbook on quantum field theory, when applying the Faddeev Popov procedure to quantize an Abelian gauge theory, they obtain the following functional ...
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Motivation for pure Yang-Mills Lagrangian
The Lagrangian for pure Yang-Mills theory is given by
$$-\frac14 F^{a\mu\nu}F^a_{\mu\nu} \tag{1}$$
where
$$F^a_{\mu\nu} = \partial_\mu A_\nu^a - \partial_\nu A_\mu^a + gf^{abc}A^b_\mu A_\nu^c.\tag{2}$$...
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Exactly what value does the Wilson line take?
Let $G$ be the Lie group of a given theory with the Lie algebra $\mathfrak{g}$.
According to the Wikipedia article, a Wilson line is of the form
\begin{equation}
W[x_i,x_f]= P e^{i \int_{x_i}^{x_f} A}
...
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Charge Renormalization in Abelian Gauge Theory under General Gauge Fixing Conditions
In scalar QED or fermionic QED, the relationship between bare quantities (subscript "B") and renormalized quantities is given by
$$
\begin{aligned}
A^\mu_B &= \sqrt{Z_A} A^\mu\,, \quad \...
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Extracting a gauge-invariant variable from a given Wilson line? (NOT Wilson loop)
Let $W[x_i,x_f]$ be the Wilson line as defined here.
Under a local gauge transform $g(x)$, it transforms as
\begin{equation}
W[x_i,x_f] \to g(x_f)W[x_i,x_f] g^{-1}(x_i)
\end{equation}
which is shown ...
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Can Black Holes with electroweak or strong interactions exists in General Relativity or in Supergravity?
During my Master's degree, we studied Black Holes as solutions of Einstein-Maxwell equations, and I was wondering if it would be possible to also add strong or electroweak forces in the classic non-...
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Are Higgs mechanism and SSB different phenomena?
In the Standard Model, the Higgs mechanism is associated with the Spontaneous Symmetry Breaking (SSB).
My understanding is that it is the Higgs field which breaks the $SU(2) \times U(1)$ symmetry at a ...
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Does LQG break gauge invariance?
So, I'm working with another researcher on a possible connection between Loop Quantum Gravity (LQG) and String Theory (ST). My colleague is proposing and insisting on a action that is not WS ...
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Commutation in the Local Gauge Transformations
Let's say that I have a Unitary Local Gauge Transformation $U$, in which the Lie Generators are $T$:
$$ \partial_{\mu} U = \partial_{\mu} e^{-i T^{a} \alpha_{a}(x)} = U \partial_{\mu} \left( -i T^{a} \...
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Interpretation of self-interacting terms in the expansion of a pure YM Lagrangian?
Let $A^{\alpha}_\mu$ be the gauge field of a Yang-Mills theory where $\alpha$ is the gauge index of generators for some Lie algebra with structure constant $C_{\alpha \beta}^\gamma$ and $\mu$ is the ...
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Dirac field coupling to gauge fields
I've seen in couple sources that the gauge invariant Lagrangian for the Dirac field being written as follows:
$$\mathcal{L} = \frac{i}{2}[\bar{\psi}\gamma^{\mu}D_{\mu}\psi-(\bar{D}_{\mu}\bar{\psi})\...
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Masses of $SU(2)$ gauge bosons
I'm currently learning quantum field theory and I'm wondering one thing.The way I understood it is that in the $SU(2)$ Yang-Mills theory, all gauge bosons have the same mass due to the spontaneous ...
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Is color charge internal symmetry or global symmetry?
I was told the color charge in the standard model could not be observed directly. This sounded like the gauge field $\vec A$ in the electromagnetism. However, it is a discrete charge and does have ...
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Noether current for Yang-Mills theory in the absence of scalar field
The theory with an arbitrary compact gauge group $G$ is given. And global transformations are valid (see below)
$$
A_{\mu}\mapsto{A^{'}_{\mu}={\omega}A_{\mu}\omega^{-1}}
$$
also $\omega \in G$ and it ...
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Geometrical interpretation of gauge fields of spin other than 2
Gravitation can be interpreted as a gauge theory with a spin 2 graviton field. This graviton field in general relativity is also interpreter as a Riemannian metric. Do other gauge theories also have ...
