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Lagrangian of a photon?

  1. Jul 11, 2015 #1
    I can't find this in any textbook, so I must not understand something about it. What is the Lagrangian of a photon? Would it be just h*nu?
     
  2. jcsd
  3. Jul 11, 2015 #2
    Photons have Spin 1. The general Lagrangian for Spin 1 particles is called the Proca Lagrangian and if put into the Euler Lagrange euquation yields the Proca equation. In addition, photons are massless. Therefore putting $m=0$ in the Proco yields the correct Lagrangian for photons. If you put this Lagrangian (i.e. the Proca with $m=0$ ) into the Euler Lagrange equation you get the inhomogeneous Maxwell equation.

    You can find the Lagrangian, for example, here
     
  4. Jul 11, 2015 #3

    Orodruin

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    There is no such thing as the lagrangian of a photon. Photons are quantum excitations of the electromagnetic field, which has a Lagrangian, essentially the lagrangian quoted by unknown1111.
     
  5. Jul 11, 2015 #4
    massless spin-1 = photon, carry only a kinitic term in L ;





    \begin{equation}

    L=-\frac{1}{4}F^{2}=-\frac{1}{4}F_{\mu\nu}F^{\mu\nu}=-\frac{1}{4}(\partial_{\mu}A_{\nu}-\partial_{\nu}A_{\mu})^{2}

    \end{equation}
     
  6. Jul 17, 2015 #5
    OK, then how does one calculate the action (S) for the amplitude of a photon?

    phi = (const) exp[(i/h_bar)S]
     
  7. Jul 17, 2015 #6

    Orodruin

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    Which part of
    was unclear? You need to specify exactly what it is you are trying to do.
     
  8. Jul 17, 2015 #7
    Feynman & Hibbs, p. 29, eqn 2.15:
     
  9. Jul 17, 2015 #8
    I can't seem to get the eqn editor to work.

    Feynman & Hibbs, p.29, eqn 2.15: phi[x(t)] = const e^(I/h-bar)S[x(t)]

    p.26: S = integral[L(x-dot,x,t) dt]

    So if a photon has no Lagrangian, how does one calculate the action, amplitude, probability, etc. for a photon?
     
  10. Jul 17, 2015 #9

    Orodruin

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    You don't. You compute the action of the electromagnetic field and correlation functions (essentially amplitudes) between different excitations of the field.
     
  11. Jul 17, 2015 #10

    Orodruin

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    Also, you are here assuming that we have the book available and ready to open. This is not getting us anywhere.
     
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