# And when not asympotic states?

1. May 6, 2013

### StarsRuler

Feynman diagrams is the standard for calculate the probability of nuclear reactions fo particles, but, when we want calculate the probability of evolution of an arbitratry field to another field a fixed time after, what is the mechanism??

2. May 7, 2013

Thanx

3. May 7, 2013

4. May 8, 2013

### DimReg

It's hard to get these things over the internet, but it looks like you are angry that no one answered your question. The truth is, it's not very clearly worded and we have to guess what you want. So here is my guess:

The rules for feynman diagrams are derived by considering asymptotic states, because asymptotic states approach free particle states. Free particle states are well understood, whereas interacting states are very poorly understood. We use feynman diagrams, based off of free particles, to try to approximate interacting states. This makes sense for scattering and decays, but for bound states it doesn't work very well. So in feynman diagrams are not powerful enough to consider arbitrary states.

For more arbitrary fields, Lattice gauge theory is used sometimes to make approximate calculations. Essentially, if you approximate space as a lattice rather than a continuum, then calculations require a lot of computational power, but are in principle well understood. Usually there is an error term proportional to the lattice spacing, so these approximations are improved by making the lattice spacing smaller, but at the cost of requiring more computational power. Using this, bound states can be considered.

5. May 8, 2013

### StarsRuler

And there is any program for calculate this in a PC?

Thanx

6. May 8, 2013

### DimReg

I don't know if any personal computers are powerful enough to do reasonable lattice calculations, but computing clusters these days can perform good calculations of this kind. One goal of such calculations is to compute the mass of the proton, which has been done to relatively high precision.

For more information, I would search for "lattice QCD". Other computer approximations are generally called "Monte Carlo simulations", which use all kinds of techniques to try to model physics in situations where feynman diagrams fail. The only technique I have any knowledge of is lattice gauge theory, so if you want to know more, you'll have to ask someone else.

Here is an introduction to lattice QCD techniques, which supposedly can be run on a personal computer. http://arxiv.org/abs/hep-lat/0506036