Saturday, October 23, 2010

Theory Update 12

After much faffing, to borrow a phrase from English climbing friends, I have decided that the best name and phase convention is this one.


That puts ordinary matter at $+ 2/9$ and mirror matter at $- 2/9$. It lets the $\overline{\nu}_{R}$ antineutrino annihilate via composition with the mirror particle $\overline{\nu}_{L}$. It gives left handed neutral particles the $+ \pi /12$ phase. Phew.

3 comments:

  1. Interesting use of the braid group B_3 on 3 strands. Using the homomorphism from B_3 to SL(2,Z) gives a nice matrix description of your particles in terms of SL(2,Z) generators:

    A=
    [1 1]
    [0 1]

    B=
    [1 0]
    [-1 1]

    This gives the following correspondences:

    nu_L = (B^-1)A
    nu*_L = B(A^-1)
    nu_R = (A^-1)B
    nu*_R = A(B^-1)

    so that, for example

    nu*_L(nu*_R)=B(A^-1)A(B^-1)=I

    as expected.

    ReplyDelete
  2. Yeah, cool kneemo. Your last result comes from drawing the picture, of course. Good to see we are getting those M theory qubit dualities sorted out, slowly.

    ReplyDelete
  3. Similar diagrams are found on page 280
    of Schiller's text on http://www.motionmountain.net/fun.html
    Are they related?

    Frank

    ReplyDelete

Note: Only a member of this blog may post a comment.