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Parity and Time Reversal symmetries.

  1. Nov 5, 2009 #1

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    I have a question, in Time Reversal operator, does an external magnetic field would get a minus sign, I guess that yes cause it changes direction, i.e if it's directed orthogonal to the surface then after time reversal I think it will direct anti-orthogonal to the surface, in Parity I don't think it would change direction.

    Is this correct?
     
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  3. Nov 5, 2009 #2

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    I have another similar question, on the same topic.
    If the hamiltonian is invariant under time reversal, [H,T]=0 then an eigenvalue of T isn't conserved.
    T is the time reversal operator.

    Now I am not sure, but an eigenvalue being not conserved perhaps means that it's absolute value squared doesnt give a positive number (which is crucial because the eigenvalues amplitudes squared represent a probability), in this case the eigenvalue, a equals: |a|^2=-1 which is impossbile.
     
  4. Nov 5, 2009 #3
    take the example of the momentum 3-vector "P" as a generic real-vector and of the angular momentum "L" (L=R^P) as a pseudo-vector.
    You can directly see how they transform under P (parity) and T (time reversal):

    P:

    • R ---> -R (R is the spacial coordinate system)
      P ---> -P
      L ----> L (unchanged)
    T:

    • R ---> R
      P ---> -P
      L ----> -L

    ...and I don't understand your second question.
     
  5. Nov 5, 2009 #4

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    Yes, I know that already, but does this mean that under parity B->B, and under time reversal B->-B?

    For my second question, what don't you understand?
     
  6. Nov 6, 2009 #5
    ah.. sorry for my digression.
    Yes, the answer is yes. You can also see that in maxwell equations, for example:
    39adeb66b53fc1be92dda9c01386c3a9.png

    as you can see, to preserve the invariance of the equation B should transform to -B (because both terms on the right change sign) under T.

    (you can check out the Jackson too..)
    I'm not even sure it is a question...
     
    Last edited: Nov 6, 2009
  7. Nov 7, 2009 #6

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    The question in my second post in this thread is proving:
    "If the hamiltonian is invariant under time reversal, [H,T]=0 then an eigenvalue of T isn't conserved."

    I am not sure what is conservation of eigenvalue.
     
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