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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Canonical quantization of abelian vector field in $R_\xi$ gauge
I am trying to do the canonical quantization of an abelian vector field $A_\mu(x)$ in the $R_\xi$ gauge. So the gauge-fixing Lagrangian is given by $$ \mathscr{L}_{gf} = -\frac{1}{2\xi} (\partial_\mu ...
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What is the link between the vector field generating the group action and the covariant derivative
I am currently working through Witten's "Two Dimensional Gauge Theories revisited". He defines an operator (p.28, but the redefinition is for p.32)
\begin{equation}
D = \sum_i \psi^i \frac{\...
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Degrees–of–freedom counting and Goldstone structure for $SU(3)$ broken by a complex $3\oplus\bar{3}$ Higgs
I am studying the Higgs mechanism in a single $SU(3)$ gauge theory with 2 scalars being a complex fundamental $\phi \sim 3$ and its complex conjugate $\psi \sim \bar{3}$. I would like to understand in ...
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Gauge dependent mass definition in perturbation theory
Let's say we describe an unstable particle using perturbation theory. Then we have a non-zero decay width, which we say $\Gamma$. Now, if we define mass to be the pole of the propagator, we get
$$
\mu^...
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Nr. of constraints and entries when considering coordinate transformation of the metric in GR
For the metric $g_{\mu\nu}$, when considering coordinate transformations, one can write:
$$g_{\alpha'\beta'}=\frac{\partial x^\mu}{\partial x^{\alpha'}}\frac{\partial x^\nu}{\partial x^{\beta'}}g_{\mu\...
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Point-splitting regularization for ghost fields
In section V of this paper, the author computes $\langle F_{\mu \nu} F^{\mu \nu} \rangle$. Using the definition of $F_{\mu \nu}$ it is not difficult to show that
$$\langle F_{\mu \nu} F^{\mu \nu}\...
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Gauge invariance in General relativity [duplicate]
Suppose a theoretical physicist wants to construct a theory to explain some newly discovered phenomenon. The new theory is expected to follow certain rules or fundamental principles. There are four ...
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Could there be multiple fields obeying the same symmetry?
For example, according to the gauge theory a massless, spin 1, Abelian field must be electromagnetic field, but could there be another field which obeys the very same Maxwell’s equation, except that ...
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Do fundamental interactions alter spacetime?
I am currently studying field theories, particularly General Relativity and Classical Electrodynamics. In the former, when one has a particle subject to a gravitational field, instead of introducing a ...
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Proving invariance of Yukawa sector under $SU(2)_L\times U(1)_Y$
As the title suggests I am trying to show this invariance. But before I do that I will explain what the crux of the problem, for me, is. This post might be a bit lengthy, but I believe it is necessary ...
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Parallel transport in Yang-Mills
I'm currently reading through David Tong's "Gauge Theory" lecture notes, and came across the following parallel transport equation:
\begin{equation}
i \frac{dw}{d\tau} = \frac{dx^\mu(\tau)}{...
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What is the physical interpretation of the target space in a $\sigma$-model?
I'm a student in the mathematical aspects of gauge theory, and I've been reading about supersymmetric $\sigma$-models as they relate to the Seiberg-Witten equations (mainly from the last chapter of ...
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Are there two meanings of small gauge transformations and why must we restric ourselves to transformations small in the first sense?
For the sake of context suppose a euclidean pure Yang Mills theory with gauge group SU(2) for the rest of this question.
The terms large and small gauge transformations are used around in two ...
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Why does the boundary behavior of Lagrange multipliers matter for gauge vs global symmetries?
In Henneaux & Teitelboim (Quantization of Gauge Systems, p. 30), they discuss the variation of a dynamical variable
$$
\delta F = \int d^nx\, u(x)\,\{F, C(x)\}_{PB},\tag{1.62}
$$
where $C(x)$ is a ...
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Gauge Invariance and Degrees of Freedom [duplicate]
According to Wigner's classification, any massless particle (except for scalars) has 2 degrees of freedom i 4D. This reduction is usually understood in terms of gauge invariance. For instance, a ...
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