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Perturbation theory and Path integrals.

  1. Jan 21, 2007 #1
    Let's suppose we have a theory with Lagrangian:

    [tex] \mathcal L_{0} + gV(\phi) [/tex]

    where the L0 is a quadratic Lagrangian in the fields then we could calculate 'exactly' the functional integral:

    [tex] \int\mathcal D[ \phi ]exp(iS_{0}[\phi]/\hbar+gV(\phi)) [/tex]

    where J(x) is a source then we could expand the perturbative exponential:

    [tex] exp(igV(\phi) \sim a(0)+a(1)g\phi +a(2)g^{2}(\phi)^{2}+...... [/tex]

    and apply functional differentiation respect to J(x) to calculate the propagators:

    [tex] <\phi (x1) \phi(x2)> [/tex]

    then, HOw the singularities or divergences arise?.
  2. jcsd
  3. Jan 22, 2007 #2


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    They arise once you compute the Green functions.

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