Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Inequality involving norm of Dirac matrix

  1. Sep 26, 2012 #1
    Hello,

    I am reading a set of lecture notes on lattice QCD:
    http://luscher.web.cern.ch/luscher/lectures/LesHouches09.pdf

    There is an inequality here i do not understand. It is numbered (1.51)
    and reads:
    [tex]
    || (1-P) D^{-1} (1-P)|| \leq || (1-P) (D^{\dagger}D)^{-1} (1-P)||^{1/2}
    [/tex]

    || ... || is the operator norm derived from the standard scalar product of Dirac
    fields.

    P is an orthogonal projector to some arbitrary subspace.

    D is a discretized version of the Dirac-operator. It is assumed that D is invertible
    and it's eigenvalue spectrum is contained in a disk in the right half of the
    complex plane, with center M+m and radius M, m and M being positive real numbers.
    Nothing else is assumed of D.

    Any idea how this inequality can be derived? I don't see it...

    Thanks...
     
  2. jcsd
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted



Similar Discussions: Inequality involving norm of Dirac matrix
  1. Matrix inequality (Replies: 1)

  2. Invariant Matrix norm (Replies: 1)

Loading...