# Perturbation theory and Path integrals.

1. Jan 21, 2007

### Kevin_spencer2

Let's suppose we have a theory with Lagrangian:

$$\mathcal L_{0} + gV(\phi)$$

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

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

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

$$exp(igV(\phi) \sim a(0)+a(1)g\phi +a(2)g^{2}(\phi)^{2}+......$$

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

$$<\phi (x1) \phi(x2)>$$

then, HOw the singularities or divergences arise?.

2. Jan 22, 2007

### dextercioby

They arise once you compute the Green functions.

Daniel.