New answers tagged gauge-theory
13
votes
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 ...
- 28.1k
13
votes
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
6
votes
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^{...
- 1,913
3
votes
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
0
votes
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
6
votes
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
3
votes
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
3
votes
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 ...
- 65k
2
votes
Motivation for adjoint representation in the Standard Model
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 ...
- 46.8k
0
votes
Can one encode topology into the position operator in quantum mechanics?
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 ...
- 790
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