# QFT - interaction between field

1. Apr 28, 2010

### paweld

Let's assume that we have two fields which doesn't interact at the beginning.
But after some time this fields start to weakly interact. Interaction lasts only finite period of time. The density of lagrangian is:
$$L = \partial_{\mu} \psi \partial^{\mu} \psi + m^2 \psi^2 + \partial_{\mu} \phi \partial^{\mu} \phi + M^2 \phi^2 + \epsilon(t) \psi \phi$$
($$\epsilon(t)$$ is different then 0 only on finite period of time)

How we could find a state of fields after interaction if we knew the state before?
How perturbative theory works when we describe evolution of system using
lagrangian not hamiltonian? Probably we first should find the fields after interaction
(from Euler equation) but how we can obtain a state?

2. Apr 29, 2010

### stephenhky

You have to use Keldysh techniques / closed-time-path integral, where a number of perturbative schemes followed.