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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Why the expectation value of three currents is important in the anomaly?
I am studying the anomalies chapter (Chapter 30) of Schwartz's [Quantum Field Theory and the Standard Model]. I want to ask why the expectation of three currents, $\langle J^\mu J^\nu J^\rho \rangle$, ...
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Quantizing the electric field without quantizing vector potential
I am trying to quantize the electromagnetic field, without using the vector potential. I start with a Fourier expansion:
$$\begin{equation}
\vec{E}(\vec{r},t) = \sum_{\epsilon} \vec{\epsilon} \int \...
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What is the relation between gauge field and Levi-Civita connection?
In field theory, covariant derivative is something like
$$D_{\mu}\phi=(\partial_{\mu}-igA_{\mu})\phi$$
while in differential geometry, covariant derivative is something like
$$D_{\mu}V^{\nu}=\partial_{...
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How are the gauge transformations of $\epsilon(\mu)$ and $A^\mu$ related?
To find a local field description of massless spin-1 particles that is Lorentz invariant, we can identify $\epsilon^\mu_{\pm}(k)$ with $\epsilon^\mu_{\pm}(k)+\alpha(k)k^\mu$. As $A^\mu$ and $\epsilon^\...
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Help understanding gauge symmetry and principal bundles
i'm diving into gauge theories and i'm having a hard time understanding the concept of Gauge symmetry.
What i understand is: gauge symmetry is the invariance of a field theory under a certain family ...
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Gauge transformation with harmonic one-form
The electromagnetic four-potential $A^{\mu}$ is not uniquely determined by the physical situation. We have the equation $$\partial^{\mu}A^{\nu}-\partial^{\nu}A^{\mu}=F^{\mu\nu}.$$
Here $F^{\nu\mu}$ is ...
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Can we prove in general that gauge fields associated with broken generators form representations of the unbroken group?
The title is a bit ambiguous. More specifically, I'm asking:
Are all coupling between massive gauge fields (associated with broken generators) and massless gauge fields of the unbroken group are in ...
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Question on the Proof of Renormalizability in Gauge Field Theory in Collins's *Renormalization*
I am currently reading Collins's Renormalization: An Introduction to Renormalization, the Renormalization Group and the Operator-Product Expansion, and have reached Chapter 12. However, I am puzzled ...
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Gauge transformation and Kaluza-Klein metric
The Kaluza-Klein metric, by reduction, can be written as a $(4+m) \times (4+m)$ symmetric matrix, where $m$ is the dimension of the additional spacetime (if we decompose $M_D = M_4 \times M_m$). It ...
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The notion of "stable mean-field state" of a spin liquid
I have some issues understanding X-G. Wen's notion of stable mean-field states of spin liquids.
I understand that the slave-boson mean-field theory is reliable when fluctuations on top of it are weak (...
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Hamiltonian formalism (with symplectic form) for time-dependent Lagrangian
I have been working on some results that work for time-independent Lagrangians $L\Big(q,\dot{q}\Big)$ and return a Hamiltonian function
$$
H(q,\dot{q})=\dot{q}^i \frac{\partial L}{\partial \dot{q}^i}-...
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Physical motivation behind gauging a global symmetry
Consider complex scalar field Lagrangian
$$\mathcal{L}=(\partial^\mu\psi)^\dagger(\partial_\mu\psi) - m^2\psi^\dagger\psi\tag{1}$$
Which exhibits $U(1)$-invariance, i.e $\psi\mapsto e^{i\alpha}\psi$. ...
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Silly confusion about gauge invariance in supersymmetric Lagrangians - in particular, in the ${\cal N}=1$ superfield formulation of ${\cal N}=4$ SYM
Hoping to resolve a simple confusion I have about supersymmetric gauge theory, one which I ran into while trying to understand the ${\cal N}=1$ superfield formulation of ${\cal N}=4$ supersymmetric ...
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Understanding 4D Gauge Fields in Compactified String Theory
Question:
I have a conceptual question regarding $4$-dimensional compactifications in string theory. For example, if we consider flat $10$-dimensional space with D$6$-branes, we obtain $7$-dimensional ...
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How to derive the gauge invariance of Yang-Mills action with external source?
In the Faddeev-Popov procedure of path integral of
$$
Z[J] = \int [DA] e^{iS(A,J)},
\quad S(A,J)= \int d^4x [-\frac{1}{4}F^{a\mu\nu}F_{a\mu\nu} + J^{a\mu}A_{a\mu} ]
$$
we have used that $S(A,J)$ is ...
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