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8 questions
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Transformation of Yang Mills Field Strength
I am confused about the expression $$F_{\mu \nu} \to F_{\mu \nu}' = U F_{\mu \nu}U^{\dagger}.$$ I found related Phys.SE posts How would one show that a nonabelian field strength tensor transforms in a ...
- 213
1
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1
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86
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Bianchi identity contradiction in Abelian case
In non-abelian gauge theory, such as P & S's chapter 15, eq. (15.89), we also have Bianchi identity.
Start with
$$\epsilon^{\mu\nu\lambda\sigma}[D_\nu,[D_\lambda,D_\sigma]]=0$$
and use $[D_\mu,D_\...
- 1,461
1
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1
answer
152
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Meaning of the notation $(D_\nu F_{\lambda\sigma})^a$ in Bianchi's identity
I'm studying Peskin and Schroeder chapter 15, on page 500, we have the Bianchi's identity in nonabelian gauge theory,
$$\tag{15.89} \epsilon^{\mu\nu\lambda\sigma}(D_\nu F_{\lambda\sigma})^a=0$$
Here $\...
- 859
0
votes
1
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242
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Commutator between covariant derivative and a field
I have field as an element of a Lie algebra as $\Phi = \phi^at^a$ and I want to calculate the commutator $$[D_{\mu}, \Phi],$$
with $$D_{\mu} = \partial_{\mu} + igA^a_{\mu}t^a,$$ the covariant ...
- 43
2
votes
3
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266
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Is the equation $[\nabla_{\mu},\nabla_{\nu}]=F_{\mu\nu}$ correct? If yes, how does it have to be interpreted?
It seems like simply using the equation
\begin{equation}
\nabla_{\mu}=\partial_{\mu}+A_{\mu}
\end{equation}
isn't enough: One obtains
\begin{equation}
[\nabla_{\mu},\nabla_{\nu}]=\underbrace{[\...
- 1,911
0
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1
answer
1k
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What is $D$ or $D$-with-a-slash-through-it in the Standard Model equation(s)?
In the mathematical formulation of the Standard Model, which I do not understand yet, there is a capital letter $D$ or $D$-with-a-slash-through-it that I can't find an explanation for.
Flip Tanedo (a ...
- 4,709
2
votes
2
answers
1k
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Gauge-covariance of the Yang-Mills field strength $F_{\mu\nu}^a$
Accordingly to Yang-Mills theories, after the introduction of a covariant derivative such that
$$D_\mu = \partial_\mu - igA_\mu, \tag1$$
you can built the kinetic term for the gauge potential $A_\...
- 1,607
0
votes
2
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637
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Notation and concepts of Yang Mills Theory
I am studying loop quantum gravity using the book by Pullin and Gambini. I am having some trouble understanding and getting past the chapter on Yang Mills theory, mainly because I am confused about ...
- 103