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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Is the gauge transformation used in Higgs mechanism concretely doing (meaning?) the same as stating that one *fixes the gauge*?
From Is the Higgs mechanism a gauge transformation or not? ( $U(1)$ context )
the answer by Florence is stating that "people are confusing gauge transformation and gauge fixing".
In the ...
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Generic form of the matter Lagrangian in QFT
It seems to me like any sensible matter Lagrangian must obey the following constraints:
It must be invariant with respect to local $SU(N)$ transformations, diffeomorphisms of the space-time manifold, ...
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In particle physics, what is the *motivation* to have invariance of a defined Lagrangian under a transformation of phase $e^{i\alpha}$ of the fields?
In particle physics, one checks the invariance of the Lagrangian under global transformations of the fields $\psi\rightarrow e^{i\alpha}\psi$ and local transformations $\psi\rightarrow e^{i\alpha(x)}\...
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QFT from the view of Principal bundles
I did read Mathematical Gauge Theory
With Applications to the Standard Model of Particle Physics, which describes the Lagrangian of Standard model by sections and connection forms of vector bundles. ...
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Gravitational instantons and normalization
The normalization factor for the gravitational instanton number is commonly stated as $1/384\pi^2$ (see for example Equation (2.27) of Dumitrescu)
$$
\frac{1}{384\pi^2}\int\text{tr}(R\wedge R)\in\...
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On gauge theories and redundant degrees of freedom
Given an action or Lagrangian with the additional information that it is a gauge system, how do we know this field has how many physical or redundant degrees of freedom? Is there any systematic method ...
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Electric gravity
Consider a model of gravity where I try to create curvature using electromagnetic fields. For that I will work with the following action
$$S[g, A] = \int d^4x \sqrt{g} g^{\mu\nu}g^{\alpha\beta}F_{\mu\...
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Describing photons with the Klein-Gordon equations
I am currently studying Introduction to Elementary Particles, by Griffiths, and in Chapter 7 (QED) he begins by stating there are essentially 3 equations we shall be using to describe particles:
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The 1-form symmetry breaking in a $(2+1)D$ $\mathbb{Z}_2$ lattice gauge theory
For a $(2+1)D$ $\mathbb{Z}_2$ lattice gauge theory:
\begin{align}
H = -\sum_{l} \tau^x_l - h \sum_p \prod_{l \in p} \tau^z_l,
\end{align}
with Gauss law $A_v \equiv \prod_{l \in v}\tau^x_l = 1$.
Here $...
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Anomaly-free theories with Weyl fermions
I'm looking at a $U(1)$ gauge theory which includes $N$ Weyl fermions all with non-zero charges. If we're careful enough with these charges, we can apparently remove all the anomalies from this theory....
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Faddeev-Popov method, insertion of identity
Question 1: Understanding the Faddeev-Popov determinant in gauge theory
In quantum field theory, we encounter difficulties when quantizing gauge theories because of redundancies in the path integral. ...
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Is $k \cdot Z_{g,h}= Z_{g,khk^{-1}}$?
In 2D CFT, $k,g,h$ are elements of some symmetry group $G$. Given a partial trace $Z_{g,h}$, what's the action of $k$ on the partial trace $Z_{g,h}$?
I heard that the group element $k$ act on the ...
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Problem in the Chern-Simons term in 4D
I'm proving some identities related to the Chern-Simons term. Specifically, I want to show that $$ \partial_\mu K_\mu = \frac{1}{16}\epsilon_{\mu\nu\rho\sigma} F_{\mu\nu}^aF_{\rho\sigma}^a,$$ when ...
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Degrees of freedom of a massive vector field
For a vector field $A^\mu$, when we introduce a mass term, gauge invariance breaks and this leads to the appearance of a longitudinal polarization state in addition to the two transverse ones. This ...
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Higgsing $SU(2)\times SU(2)\rightarrow U(1)$
I'm wondering how to interpret the following setup: consider a bi-fundamental Higgs field living in the representation $(2,2)$, which has the transformation property
$$
\Phi_{i \alpha} \rightarrow \...
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