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Does Schroedinger Eat Goldstone too?

  1. Feb 26, 2012 #1
    Note the wave function in the Schroedinger Equation has phase freedom from 0 to 360 degrees.

    Imagine the Mexican Hat thing or potential well.
    http://www.nature.com/nphys/journal/v7/n1/images/nphys1874-f1.jpg

    When a double slit emitter is shut off. The phase is at the center of the hat or well.
    When it turns on. The phase chooses a value (akin to falling to the ground state of the hat). This means wave functions are example of spontaneous symmetry breaking. So where is the goldstone boson in QM?

    Please give another example in quantum mechanics where the concept of spontaneous symmetry breaking is used. Goldstone Theorem says that whenever a symmetry breaks, goldstone bosons appear. In the wave functions, the phases are the degrees of freedom that breaks from the symmetry.

    Also perhaps one can consider a particle as the symmetry or at the center of the hat or well. When it turns to wave, there is a phase degrees of freedom. Has anyone heard of this before, if so, please share papers or references about it. Thanks.
     
  2. jcsd
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