Content deleted Content added
m Better description. |
|||
| (One intermediate revision by one other user not shown) | |||
Line 1:
{{short description|Class of operators in
In [[statistical mechanics]] and [[quantum field theory]], a '''dangerously irrelevant operator''' (or '''dangerous irrelevant operator''') is an [[operator (mathematics)|operator]] which is irrelevant at a renormalization group fixed point, yet affects the [[infrared]] (IR) physics significantly (e.g. because the [[vacuum expectation value]] (VEV) of some field depends sensitively upon the coefficient of this operator).
Line 21:
== Other uses of the term ==
Consider a renormalization group (RG) flow triggered at short distances by a relevant perturbation of an ultra-violet (UV) fixed point, and flowing at long distances to an infra-red (IR) fixed point. It may be possible (e.g. in perturbation theory) to monitor how dimensions of UV operators change along the RG flow. In such a situation, one sometimes<ref>{{Cite journal|last=Gukov|first=Sergei|date=2016-01-05|title=Counting RG flows|journal=Journal of High Energy Physics|language=en|volume=2016|issue=1|pages=20|arxiv=1503.01474|doi=10.1007/JHEP01(2016)020|bibcode=2016JHEP...01..020G |s2cid=23582290|issn=1029-8479}}</ref> calls dangerously irrelevant a UV operator whose scaling dimension, while irrelevant at short distances: <math>\Delta_{\rm UV}>d</math> , receives a negative correction along a renormalization group flow, so that the operator becomes relevant at long distances: <math>\Delta_{\rm IR}<d</math>. This usage of the term is different from the one originally introduced in statistical physics.<ref>{{Cite journal|last1=Amit|first1=Daniel J|last2=Peliti|first2=Luca|date=1982|title=On dangerous irrelevant operators|journal=Annals of Physics|language=en|volume=140|issue=2|pages=207–231|doi=10.1016/0003-4916(82)90159-2|bibcode=1982AnPhy.140..207A }}</ref>
==References==
| |||