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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Non-invertible symmetries: Half gauging and 't Hooft lines
In (2.27) of https://arxiv.org/abs/2205.05086, when performing a gauge transformation of the background gauge field $B \to B +d \Lambda $, the 't Hooft line $H(\gamma)$ transforms as
\begin{equation}
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Unitarity and renormalizability in $R_\xi$ and 't Hooft gauge
Consider the massive propagator with gauge fixing $\frac{1}{2a} (\partial A)^2$
$$
\Delta_{\mu\nu}=-i\left[\frac{g_{\mu\nu}}{k^2-m^2}-\frac{k_\mu k_\nu}{m^2}\left(\frac{1}{k^2-m^2}-\frac{1}{k^2-am^2}\...
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Abelian Chern-Simons large gauge transform
My question concerns the $U(1)$ Chern-Simons theory with the action
$$S = \frac{k}{2\pi}\int A\wedge \mathrm{d}A.$$
In my lecture, it is stated that:
A large gauge transformation involves taking $A\...
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In the local $U(1)$ symmetry , does the inverse projection map of each point is onto the tangent plane at the point?
Does a $U(1)$ local symmetry on a non-flat spacetime, say a sphere, imply that a point on the sphere is equivalent to a circle (corresponding to the phase) on the tangent space to that point?
Does ...
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Meaning of “transforms like the adjoint” in the context of Yang Mills Theory and connection to Lie Algebra
In Srednicki Chapter 69, we say something transforms like the adjoint if its transformation under the $SU(N)$ group action is $$W\rightarrow UWU^\dagger$$ The Field strength and the covariant ...
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Connection between Noether's theorem for gauge theories and 1-form symmetries?
Applying Noether's theorem to a gauge theory, one can show that the conserved current is generically of the form
$$J^\mu=\partial_\nu k^{[\mu\nu]},$$
such that the conserved charge is really ...
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Effect of gauge-fixing via Lagrange multipliers on Euler-Lagrange equations
Preamble
Consider the Lagrangian density for electrodynamics:
$$L=-\frac{1}{4}F^{\mu\nu}F_{\mu\nu}-A_\mu J^\mu\tag{1}$$
With the usual definition of $F_{\mu\nu}=\partial_\mu A_\nu - \partial_\nu A_\mu$...
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Counting of degrees of freedom in Higher Spin Theories in curved spacetime
In 4d Minkowski, a (bosonic) tensor field with spin $s\in\mathbb{N}_+$ are constrained by Poincaré symmetry, and the physical degrees of freedom can be counted by considering the little group: a spin-$...
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Can we impose Coulomb gauge without using temporal gauge in source-free Maxwell electrodynamics?
Coulomb gauge is $$\vec{\nabla} \cdot A=0$$ Now, from expression for electric field in terms of potentials $\vec{E}=-\vec{\nabla} \phi-\frac{\partial \vec{A}}{\partial t}$ and Gauss Law $\vec{\nabla} \...
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What makes electric and magnetic fields in Yang-Mills theories gauge co-variant?
Specifically in QCD, why is it so?
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Seeking references for giving geometrical interpretations of electromagnetism and the nuclear forces
From this thread, we have the following comment:
To further blur the line, it is possible to give geometrical interpretations of electromagnetism and the nuclear forces, such that they appear to be ...
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Gauging a finite non-abelian global symmetry in 2D
Consider a 2D system with a non-anomalous finite non-abelian global symmetry $G$, for example $$G = S_3=\{e,a,a^2,b,ab,a^2b\}$$ with $a^3=b^2=1$. One expects the local operators charged under the ...
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Is the bundle of the Aharonov-Bohm effect like the tangent bundle of a cylinder or like the tangent bundle of a truncated cone?
Both are trivial bundles, and the natural (metric) connection is flat (curvature-free) for both. The difference between them is that the holonomy of the tangent bundle of the cylinder is trivial while ...
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How is classical Chern-Simons theory topological?
Note: I am using "global" and "topological" somewhat interchangable. This seems to be the case in texts and papers, but please point out if this is inappropriate.
Classical Chern-...
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What is a gauge transformation? How does it relate to Cauchy intial value problem and second functional derivative of the action?
I am having conceptual problems about 'gauge transformation'. I have well heard that gauge trnasformation is a 'local symmetry' and 'fake symmetry', but I want to understand it more precisely.
I am ...
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