What is the difference between singularity and infinity in QTF theo?

[ndung200790]

Please teach me this:
What is the difference between singularity and infinity points.Because we often encounter with infinity counterterms in QTF theory,but trying to avoid the singularity counterterms.
Thank you very much in advanced.

 

[A. Neumaier]

Please teach me this:
What is the difference between singularity and infinity points.Because we often encounter with infinity counterterms in QTF theory,but trying to avoid the singularity counterterms.

Your question is difficult to interpret.

A singularity is usually a point where a quantity in the physical model gets infinite. Whereas the infinities in QFT arise only due to sloppy model building, and are not there in the carefully defined renormalized theory.

 

[Quantumjump]

Please teach me this:
What is the difference between singularity and infinity points.Because we often encounter with infinity counterterms in QTF theory,but trying to avoid the singularity counterterms.
.

Well, i don't know if what you mean is really what i am thinking about, but as far as I know I can say this: in physics, unlike maths, there is basically just one kind of infinity , so it's not like in math where you have areas of set theory/number theory making distinction between aleph_zero and aleph_one, for example, as two completely distincts type of infinity, namely, the cardinality of integers and of real numbers respectively.

However, even if in physics there is just one type of infinity, it can emerge in at least two different ways. More specifically, in QFT, infinities can first emerge from the way ypu define commutations relations:this is typically the case that happen when quantize a Klein-Gordon field, for example: it a term delta(0) appears at the end of the calculation, but delta(0) = infinite, so we introduce normal-ordering to get rid of that term.

Another way "infinities" can emerge , aside of that, is from functions that MIGHT potentially an infinite behavior at some values of the independant variable : this is because , for example, they have a denominator. A typical example is the Feynman propagator, which describes the transmission of an interaction from a point to another. Here singularities are a terminology that comes from the language of Complex Analysis (as the Feynman propagator is a complex function). In this case, singularities and poles have a deep physical meaning, unlike the delta(0) i mentioned earlier in the previous case which was just a pathology risen from the absence of time-ordering in commutation relations.

I have not mentioned renormalization but I don't think you meant that topic.

does it answer your question? Hope this will help.