Doubt with differential forms

  • Thread starter Dox
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  • #1
Dox
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Main Question or Discussion Point

Hi everyone, I've been studying a paper in which there is a connection given by,

[tex]A = f(r)\sigma_1 dx+g(r)\sigma_2 dy,[/tex]​

where [tex]\sigma[/tex]'s are half the Pauli matrices. I need to calculate the field strength,

[tex]F = dA +[A,A][/tex].​

I have computed it, but a factor is given me problems. I would say,

[tex]dA = f' \sigma_1 dr\wedge dx + g'\sigma_2 dr\wedge dy[/tex]​

and

[tex][A,A] = 2 f g \sigma_3 dx\wedge dy,[/tex]​

with a factor 2 coming from the fact that there are two contributions... like a binomial.

Is it OK or there is a half factor hidden in the definition of [tex][A,A][/tex]?

Thank you so much.

DOX​
 

Answers and Replies

  • #2
martinbn
Science Advisor
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511
There aren't two contributions. They are in the commutator of the sigmas.
 

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