(March 4, 2017 at 7:36 am)Alex K Wrote: What we have here is the so-called path integral of the Standard Model of particles physics, embedded in a quantized version of Einstein's General relativity.
There's one symbol hidden in this very formula which indicates that this description is not complete. It's the upper case letter Lambda (looks like an A without the cross bar) right below the first integral sign (the big S).
k < Lambda tells you that we only take into account energies below the so-called cutoff energy scale Lambda, and ignore any goings-on higher than lambda. This is necessary because general relativity is what is called non-renormalizable - it contains infinities as you go to arbitrary large energies which cannot be gotten rid off in a consistent manner unless you introduce an infinite amount of paramters into the theory.
Strictly speaking, once we have this cutoff scale in the path integral, we need to include a whole infinite tail of additional terms into this formula to really capture the complete physics as observed at low energies. As long as we study processes at energies far below the cutoff energy lambda, these additional terms contribute less and less to the physical goings-on and can be neglected to very good precision. But the necessity to have Lambda at all shows us the incompleteness of quantum gravity which is so often talked about.
Yeah, that's what I meant. Really it is.
Boru
‘But it does me no injury for my neighbour to say there are twenty gods or no gods. It neither picks my pocket nor breaks my leg.’ - Thomas Jefferson
