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Thread: A question in QFT of Weinberg

  1. #1 A question in QFT of Weinberg 
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    The complete electron propagator is S=[p+m -sigma]^-1 .
    where the higher order corrections to the propagator is to replace the electron mass m by m-sigma.Here sigma is a function of p and m.Then they saids: so the effect of these corrections on matrix elements of the operator psi bar.psi between one electron states of four momentum p is to multiply them by a factor:

    F(p)=1-(d sigma(p,m)/dm) at m=0.Then I do not understand whyS=[p+m-sigma]^-1=([p+m]^-1)(1-(d sigma/dm))
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  2. #2  
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    Quote Originally Posted by dungnguyen View Post
    The complete electron propagator is S=[p+m -sigma]^-1 .
    where the higher order corrections to the propagator is to replace the electron mass m by m-sigma.Here sigma is a function of p and m.Then they saids: so the effect of these corrections on matrix elements of the operator psi bar.psi between one electron states of four momentum p is to multiply them by a factor:

    F(p)=1-(d sigma(p,m)/dm) at m=0.Then I do not understand whyS=[p+m-sigma]^-1=([p+m]^-1)(1-(d sigma/dm))
    Give me a page number.
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  3. #3  
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    Page 144 ,The Quantum Theory of Field Vol 2 of Weinberg
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  4. #4  
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    Sorry. I don't have volume 2.
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  5. #5  
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    Quote Originally Posted by dungnguyen View Post
    The complete electron propagator is S=[p+m -sigma]^-1 .
    where the higher order corrections to the propagator is to replace the electron mass m by m-sigma.Here sigma is a function of p and m.Then they saids: so the effect of these corrections on matrix elements of the operator psi bar.psi between one electron states of four momentum p is to multiply them by a factor:

    F(p)=1-(d sigma(p,m)/dm) at m=0.Then I do not understand whyS=[p+m-sigma]^-1=([p+m]^-1)(1-(d sigma/dm))
    Those equations are pretty seriously mangled -- you left out many symbols! But your reference to page 144 was enough of a clue to at least figure out what you meant to write at the beginning.

    The corrections to the electron propagator amount to a substitution of a diminished mass for the electron mass. That manoeuvre, in turn, is equivalent to multiplication of the matrix elements of the operator by F(p). That isn't the same as multiplying the propagator by F(p).
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  6. #6  
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    Please demontrate ''That manoeuvre,in turn,is equivalent to multiplication of the matrix elements of the operator by F(p)''
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  7. #7  
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    Quote Originally Posted by dungnguyen View Post
    Please demontrate ''That manoeuvre,in turn,is equivalent to multiplication of the matrix elements of the operator by F(p)''
    Are you asking how to perform a matrix multiplication?
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  8. #8  
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    I am asking about why the the matrix must be multiplied with F(p) after the correction to the mass of electron.
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