Advances in Theoretical Physics and Mathematics: The Renormalization Group

To understand the renormalization group, first you need to understand calculus. To understand calculus, first your need to understand arithmatic.

Calculus is what is called ‘advanced arithmatic’. Its a shortcut for when you need to add alot of numbers ( a whole lot) so you invent symbol for this — call it a collection.

I did this recently — -i decided to add alot of pennies to turn them into dollars and even went to a bank to get these things you put them in. (Someone who denied it had already stolen all my other pennies ; i spent an hour or so counting them up — and then i realized i could go to a store and they have amachine which does that. I did that and got 4$ — bought tea and a can of vegetables. )

Renormalization group is just advanced calculus. There are 2 or several main approaches. Most famous is Feynman’s ‘QED’ — but this deals with things i can’t see nor really understand — photons, virtual particles, all sorts of subatomic particles. (I can see photons especially in day time but can’t really mathematize that.)

Mayer had a similar formalism for molecules — -how do you add up all the molecules and the way they interact? That leads to Mayer cluster diagrams — -similar to Feynman path integrals but ‘classical’. All you are doing is adding apples and oranges, not pions and neutrinos (which don’t grow in my area).

K G Wilson and Kadanoff did renormalization via block chains (see arxiv). This concept is no different than looking at a computer screen really close up — all you see is noise — and then move back, and you notice it turns into letters — apparently messages from god, the dog, or the space aliens — or picutres (‘you wanna see my picture? ).

Arithmatic, calculus and renormalization have what are called ‘group’ properties. All numbers are part of a group, and so are the patterns used in calculus (curves, manifolds) and renormalization (crystals, fractals, etc.(