2
$\begingroup$

A generating set of a semigroup(monoid) is a subset of the semigroup set such that every element of the semigroup can be expressed as a combination (under the semigroup operation) of finitely many elements of the subset. Elements of the generating set of a semigroup(monoid) are called generators of the semigroup.

One example of a renormalization group with an infinite number of generators is the Kadanoff-Wilson block-spin transformation in statistical mechanics. The renormalization group with infinite number of generators satisifies the renormalization group flow equations.

Is there any renormalization group with infinite number of generators that does not satisify any renormalization group equation ?

Improve this question
$\endgroup$
3
  • 3
    $\begingroup$ (1) The (poorly named) renormalization group is not a group in a mathematical sense. (2) The renormalization group refers to a set of functional differential equations that describe how various observables depend on the renormalization scale. Generally there are an infinite set of couplings involved in the renormalization group flow. Given (1) and (2), I am not sure I understand what you are asking in your question. $\endgroup$
    – Andrew
    Commented Apr 23 at 0:52
  • $\begingroup$ @Andrew generator can be defined as elements of semigroup that can construct the set underlying the semigroup or all elements of the semigroup. Yes, I should give a definition, and I have updated the question by giving a definition of generator. $\endgroup$
    – XL _At_Here_There
    Commented Apr 23 at 2:12
  • $\begingroup$ @Andrew and I am not sure I understand what you mean by "The renormalization group refers to a set of functional differential equations that describe how various observables depend on the renormalization scale. " Could you clarify what you mean, or give an example to explanation. $\endgroup$
    – XL _At_Here_There
    Commented Apr 23 at 2:15

0

Reset to default