Linked Questions

14
votes
3answers
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....
30
votes
2answers
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). ...
14
votes
1answer
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 ...
12
votes
3answers
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 ...
6
votes
2answers
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 ...
3
votes
3answers
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 ...
3
votes
1answer
440 views

Gauge invariance of $\theta$-term in QCD

I have a problem with the $\theta$-term in the QCD-Lagrangian $$ \mathcal{L} = \overline{q}(x)i\gamma_\mu{D^\mu} q(x)-\overline{q}(x)\mathcal{M}q-\frac{1}{4}F^a_{\mu\nu}F_a^{\mu\nu}+ \theta \frac{g^...
2
votes
1answer
312 views

Gauge transformations at infinity

Consider the following paragraph taken from page 15 of Thomas Hartman's lecture notes on Quantum Gravity: In an ordinary quantum field theory without gravity, in flat spacetime, there two types of ...
5
votes
1answer
223 views

Gauge transformation and large gauge transformation

Recently, Strominger posted his lecture notes on the infrared structure of gravity and gauge theory 1703.05448. In section 2.5, the equation (2.5.16) takes the following form $$e^2\partial_zN=A_z^{(0)...
1
vote
1answer
184 views

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 ...
5
votes
1answer
111 views

What justifies compactifying space and spacetime, in the context of instantons?

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 \...
1
vote
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 $$F_{\mu\nu}\tilde{F}^{\mu\nu}=\partial_{\mu}(\epsilon^{\nu\nu\lambda\rho}A_\nu F_{\lambda\rho}).$$...
3
votes
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 ...
1
vote
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 ...
0
votes
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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