3k views

What is the basis of gauge theory?

I’m learning about gauge concepts. I’ve always had the idea that by looking at a phenomenon from different viewpoints, that symmetries could be derived – in fact, that was what an equal sign signified....
4k views

Large and small gauge transformations?

I've a questions about the difference between small and large gauge transformations (a small gauge transformation tends to the identity at spatial infinity, whereas the large transformations don't). ...
2k views

Does magnetic monopole violate $U(1)$ gauge symmetry?

Does a magnetic monopole violate $U(1)$ gauge symmetry? In what sense and why? Insofar as I know, there are at least two types of magnetic monopoles. One is the Dirac monopole while the other is the ...
746 views

Why are topological properties described by surface terms?

An example are the anomalies in abelian and non-abelian gauge quantum field theories. For example, the abelian anomaly is $\tilde {F}_{\mu\nu}F^{\mu\nu}$ and the integral over this quantity is a ...
1k views

Making the connection between gauge theory and fiber bundles precise

When people talk about the gauge theory and fiber bundles, mostly what is talked about is simply the group and the connection that is put on the principal bundle. But the principal bundle has a ...
571 views

Physical meaning of gauge choice in electromagnetism

In electromagnetism, it is often referred to gauges of the electromagnetic field, such as the radiation or Coulomb gauge. As far as I know, the definition of a gauge helps us to redefine the problem ...
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Boundary Conditions giving Gauge Transformation a Physical Meaning?

I am currently reading Robert Laughlin's Nobel lecture. In the part where he uses gauge invariance to explain integer quantization of the Hall conductivity, he has a 2D rectangular surface which is ...
111 views

When studying Yang-Mills instantons, there are two instances where one compactifies a space. When classifying vacuum states, one demands $A_\mu(\mathbf{x})$ to become a constant as $\mathbf{x} \to \... 1answer 127 views Is it enough to assume$F_{\mu\nu}\to 0$at infinity but not$A_\mu$to derive the equation of motion? Suppose the the Lagrangian$\mathscr{L}$of the free electromagnetic field is augmented with the term $$F_{\mu\nu}\tilde{F}^{\mu\nu}=\partial_{\mu}(\epsilon^{\nu\nu\lambda\rho}A_\nu F_{\lambda\rho}).$$... 0answers 117 views Compactification of space in Hamiltonian formulation of Yang-Mills theory I am reading David Tong's lecture notes on Gauge Theory where he talks about Hilbert space interpretation of Yang-Mills theories in Section 2.2 of Chapter 2. When discussing the gauge dependence of ... 0answers 98 views Boundary condition of$SU(2)$gauge theory Consider$SU(2)$gauge theory. The classical ground state is$F^a_{μν}=0$. This implies that the vector potential$A^a_μ=U∂_μU^†$. Here$U(x)$is an element of the gauge group. Why can we impose the ... 0answers 96 views Classical Vacua Consider$SU(2)$gauge theory. The classical ground state is$F^a_{μν}=0$. This implies that the vector potential$A^a_μ=U∂_μU^†$. Here$U(x)$is an element of the gauge group. Now suppose that$U_0(...

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