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Orthogonal and linear

  1. Sep 4, 2007 #1
    I was reading the literature, and come across this. But I couldn't decipher what it means by linear combination and orthogonal combination.

    It is sufficient to consider two axionic fields, A and B, with a potential:

    [tex] V = \lambda_{1}^4 [1 - cos(\frac{\theta}{f_1} + \frac{\rho}{g_1})] + \lambda_{2}^4 [1 - cos(\frac{\theta}{f_2} + \frac{\rho}{g_2})][/tex]

    It is easy to see that, when the condition

    [tex]\frac{f_1}{g_1} = \frac{f_2}{g_2}[/tex]

    is met, the same linear combination of the two axions appears in both terms. Hence, the orthogonal combination is a flat direction of V.
     
    Last edited: Sep 4, 2007
  2. jcsd
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