# Tag Info

### How can coordinates be meaningless in General Relativity?

The quote that prompted this question is my fault, so perhaps I should answer this. In context I wrote [C]oordinates are meaningless. You can calculate any physically meaningful quantity using any ...
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### How can coordinates be meaningless in General Relativity?

Coordinates are not meaningless. But perhaps a better word would be unimportant - in the sense that the physics does not care what coordinate system you use and all measurements that you could make ...
• 135k

### How can coordinates be meaningless in General Relativity?

Aidan Beecher asked: "Why isn't it possible to find any choice of coordinates that correspond to a particular observer, like in special relativity, where it is possible to Lorentz transform into ...
• 12.5k
1 vote
Accepted

### Derivation of the BRST invariance in QCD

Your problem is that your equation $$\delta D^{ab}_{\mu} = \delta^{ab} \partial_{\mu} \delta + gf^{abc}\left[\epsilon D^{cd}_{\mu} \omega_{d} \right],$$ is wrong. The correct version is  \delta D^{...
Accepted

### Is string theory a particular non-commutative field theory (whether the commutator of the position coordinates in string theory is non-zero)?

The relation between string theory and non-commutative geometry is very poorly understood. Non-commutativity is only seen when studying open strings. The positions of close $N$ D-branes is described ...
• 76

### Can Maxwell's equations be generalized to all fields?

To add a bit to the story: Any conserved four vector implies the mathematical existence of fields satisfying Maxwell's equations [1]. For this reason, I like to think of Maxwell's equations as an ...
• 773
Accepted

### Why is the gauge field $A_\mu$ real for $\mathrm{U}(N)$ symmetry?

The first point is that the Lie group $G=U(N)$ [which consists of unitary $N\times N$ matrices] is a real Lie group, which is perhaps best explained as that the tangent spaces, or equivalently, the ...
• 208k

### Why is the gauge field $A_\mu$ real for $\mathrm{U}(N)$ symmetry?

First, I question the importance of this in practice. Because if you have an action where the $A_\mu^a$ are initially real and you decide that you don't like this, you can always change this by ...
• 8,371
Accepted

### Motivation for adjoint representation in the Standard Model

Nonabelian gauge groups that you are considering are all conceptual descendants of the SU(2) of isospin (1954), a classic paper you may have gone through. Generalization to higher N groups SU(N) is ...
If you have a (Lie) symmetry, there will be generators. In particular, in the case of Lie symmetries, the generators - say $\sigma_x,\sigma_y,\sigma_z$ - connect states in the Hilbert space that ...
Mathematically the data of the topology is encoded in the structure of the operators themselves. I will focus on the simple case of the punctured plane $M=\mathbb{R}^2\setminus \{0\}$. Suppose we are ...