🚀 go-pugleaf

In article <MATT.92Nov8225553@physics16.berkeley.edu> matt@physics.berkeley.edu writes:
>In article <23767@galaxy.ucr.edu> baez@ucrmath.ucr.edu (john baez) writes:
>
>> In solid state you have
>> quite a bit of choice in terms of finding systems that have roughly some
>> Lagrangian or other, so you can really test your mathematical notions to
>> some extent.  (Typically, of course, the real condensed matter system is
>> more complicated than the Lagrangian you guessed for it, so these "tests"
>> are always suspect.)
>
>Oh, but that's the whole point of a renormalization group analysis,
>right?  You just show your Lagrangian includes all of the relevant
>parameters.
>
>In a sense, I think that the renormalization group justifies, in
>retrospect, a lot of what physicists have done for over a century:
>modeling a very complicated system by a simple mathematical
>description.

Hmm.  It's a good point but I don't think the renormalization group
hides all sins.  That is, I'm sure there are plenty of solid state
physics problems where you say "The Lagrangian is probably like this..."
and calculate something, decide that you're getting the wrong answer,
and say "Hmm, maybe I should try a different Lagrangian - oh yeah, I
must've neglected the Flugenhasen effect, which we can model by an extra
term of the form...."  It seems, for example, that that's been going on
a fair amount in the efforts to understand high-Tc superconductivity.

Now, why is this true?  Well, for one, probably because in solid state
you never show your Lagrangian includes all the *possibly* relevant
parameters; there are simply way too many, iron atoms (e.g.) having lots of
degrees of freedom.  You instead guess and hope that you have got all
the relevant parameters.

Also - and here I am on shaky ground - there is more to life than
critical points, and renormalization group analysis doesn't answer every
question you might dream up about what's going on away from critical
points - I don't think.