Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Quantum filed theory in 1+1 dimension

  1. Aug 18, 2011 #1
    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?
  2. jcsd
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?