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Wave eq., two real fields with interaction, wave speed.

  1. Sep 16, 2009 #1
    Say we have two real fields, R(x,t) and S(x,t), which satisfy the 3-dimensional wave equation. Now let there be an interaction potential between the fields R and S of the form, V = m(R-S)^2.

    Suppose the "motion" of the fields is either symmetric or anti-symmetric, that is R(x,t) = + or - S(x,t).

    Then is it true we will have mass-less modes when R and S are symmetric and massive modes when R and S are anti-symmetric?

    A one-dimensional example, two superimposed strings with a potential V proportional to the area between the strings squared?

    Thank you for any help.
  2. jcsd
  3. Sep 17, 2009 #2


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    I believe that is "correct". However, mass is a result of quantization. If they're just classical fields, then I believe you should replace "mass" with "attenuation (constant)". Oh, and "the wave equation" should be relativistically invariant (or covariant if R and S have internal structure).
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