Let's suppose we have a theory with Lagrangian:(adsbygoogle = window.adsbygoogle || []).push({});

[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?.

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# Perturbation theory and Path integrals.

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