# Quantum filed theory in 1+1 dimension

1. Aug 18, 2011

### paweld

Is it true that in 1+1 dimensional Minkowski spacetime scalar quantum filed theory defined
by the lagrangian (in the interaction picture, so that the normal ordering makes sense):
$$\mathcal{L} = : \frac{1}{2} (\partial_\mu \phi) (\partial^\mu \phi) - \frac{1}{2} m^2 \phi^2 - \frac{1}{4!} \lambda \phi^2 :$$
is finite, i.e. all Feynman graphs which can be constructed in this theory give finite result?

What about the series one obtains summing corrections coming from all orders of loop expansion?
Is there any proof that in case of this theory the perturbation series is convergent?

It is said that the people who work in constructive quantum filed theory managed to show
the existence of the interacting filed in 1+1 and 2+1 dimension. What is the the idea of
their proof?

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