Arcadian Functor

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Marni D. Sheppeard

Monday, March 22, 2010

M Theory Lesson 307

Such Hermitian matrices provide a basis for all $3 \times 3$ Hermitian $1$-circulants in the form Since the eigenvalues of each basis matrix take the values $(1,1,-1)$, the eigenvalues of the sum are of the form
$\lambda_1 = \alpha + \beta - \gamma$
$\lambda_2 = \alpha - \beta + \gamma$
$\lambda_3 = - \alpha + \beta + \gamma$
providing an alternative characterisation of mass triplets, replacing Brannen's $v$, $s$ and $\theta = 2/9$ with
$v = \alpha + \beta + \gamma$
$s = \frac{2 \gamma}{1.10265678}$
Note that when the Hermitian matrix is corrected by the appropriate phased diagonals, it arises as the Fourier transform of a circulant with only three non zero entries, representing the mass triplet. This Hermitian basis is only slightly different from the one derived by Brannen in his recent paper on generations.


Blogger anvesh kadimi said...

hi can you post your all m theory lessons blogs please they are very useful

March 23, 2010 12:55 AM  
Blogger Kea said...

Anvesh, I will think about sorting things better, but it is tricky because Google have limited the Blogger options.

March 23, 2010 9:26 AM  
Blogger anvesh kadimi said...

ok can u send them to my mail id
please thanks

March 26, 2010 12:53 PM  

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