4
votes
1answer
52 views
IR divergence and renormalization scale in dimensional regularization
Is it possible that if a certain (loop) integral is IR divergent then that will have effect on the dimensionally regularized answer for that? (..does the epsilon expansion see the IR divergence in ...
3
votes
1answer
110 views
What does it mean to renormalize an effective field theory?
This is in reference to slide 19 here http://cosmology.lbl.gov/talks/Pajer_13.pdf
"As always in Effective Field Theory, the theory becomes predictive when there are more observables than parameters"
...
3
votes
0answers
47 views
Renormalization group equation of 1D charge susceptibility
I am readng the famous book Quantum Physics in One Dimension by Thierry Giamarchi ,where I have a subtle question about the Renormalization group equation of 1D charge susceptibility at the end of ...
1
vote
1answer
90 views
Integrating out high momentum modes in $\phi^4$ theory
I'm trying to follow section 12.1 of Peskin & Schroeder, which describes how integrating out the high momentum modes of the field in $\phi^4$ theory transforms the Lagrangian both by changing the ...
1
vote
0answers
44 views
Anomalous dimension for bare actions with a standard kinetic term
In this paper on p42, it is explained that when starting with a bare action that contains a standard kinetic term, this kinetic term attains a correction in the course of the RG flow which can be ...
2
votes
1answer
136 views
+50
How (why!?) does one introduce an UV cut-off in dimensional regularization?
This question is in reference to the confusing equation 3.7 (page 14) of this paper.
One sees the 1-loop answers in their theory as given in their A.7 and A.8 on page 20. Each of the terms is a ...
6
votes
0answers
53 views
What is energy in $z \neq 1 $ theories?
In a critical theory with dynamical critical exponent $z \neq 1 $, which amongst frequency, $\omega$, and dispersion, $E(\vec{k})$, may be referred to as ''energy''? I'm confused about this since in ...
2
votes
0answers
41 views
Relevant operators in two dimensional O(n) models
The most general hamiltonian of a two dimensional $O(n)$ and $Z_2$ invariant statistical model can be written:
$$
H=\int d^2 x \left[\frac{\nabla \mathbf{\phi}^2}{2} + \frac{m_0^2}{2}\mathbf{\phi}^2 ...
4
votes
1answer
81 views
Beta-function non-zero at classical level?
In Jaume Gomis's lecture 5 on CFT at Perimeter Institute, he says (at 27:40 minute mark) that the beta function, classically, of the $m^2$ parameter in massive $\lambda \phi^4$ theory is
$$\beta(m^2) ...
5
votes
0answers
94 views
Setting of renormalization scale in field theory calculations
In dimensional regularization an arbitrary mass parameter $\mu$ must be introduced in going to $4-\epsilon$ dimensions. I am trying to understand to what extent this parameter can be eliminated from ...
4
votes
1answer
100 views
Can Divergences in Nonrenormalizable Theories Always Be Absorbed by (An Infinite Number of) Counterterms?
For example, consider the $\phi^3$ theory in $d=8$, with Lagrangian:
$\mathcal{L}=\frac{1}{2}\partial_{\mu}\phi\partial^{\mu}\phi-\frac{1}{2}m^{2}\phi^{2}-\frac{1}{3!}\lambda_{3}\phi^{3}$.
In 8 ...
1
vote
1answer
84 views
Renormalizibility by power counting
When testing a theory for its renormalizability, in practice one always calculates the mass dimension of the coupling constants $g_i$. If $[g_i]>0$ for any $i$ the theory is not renormalizable. I ...
3
votes
2answers
147 views
Renormalization condition: why must be the residue of the propagator be 1
In on-shell scheme, one of the renormalization conditions is that the propagator, say, a scalar theory
$$\frac{1}{p^2+m^2-\Sigma(p^2)-i\epsilon}$$
must have a unit residue at the pole of ...
2
votes
1answer
100 views
physical importance of regularization in QFT?
The standard lore in QFT is that one must work with renormalised fields, mass, interaction etc. So we must work with "physical" or renormalised quantities and all our ignorance with respect to its ...
1
vote
1answer
99 views
Degree of divergence of a Feynman diagram
I am studying the degrees of divergence of Feynman diagrams. I feel that I miss something but I don't really understand what. Please apologize if this question is silly. Anyway.
As an introduction to ...
4
votes
1answer
185 views
One-loop $\phi^4$ theory in $d = 3$
I'm trying to calculate the 1 loop correction to the propagator in massless $\phi^4$ theory, in $d = 3$, just for fun. The diagram just looks like a straight line with a circle touching tangently to ...
4
votes
1answer
143 views
What does it mean to integrate out fields from a theory?
I've done a fair bit of reading on this subject and I'm still confused about the basic principle of integrating out fields in QFT. When we have a function of 2 fields a and b, f(a,b), and we integrate ...
4
votes
2answers
104 views
Dimensional Regularization involving $\epsilon^{\mu\nu\alpha\beta}$
Is it possible to dimensionally regularize an amplitude which contains the totally antisymmetric Levi-Civita tensor $\epsilon^{\mu\nu\alpha\beta}$?
I don't know if it's possible to define
...
6
votes
1answer
113 views
Why is $R^2$ gravity not unitary?
I have often heard that $R^2$ gravity (as studied by Stelle) is renormalisable but not unitary. My question is: what is it that causes the theory to suffer from problems with unitarity?
My naive ...
2
votes
1answer
94 views
Symmetries in Wilsonian RG (2)
This question is related to the paper http://arxiv.org/abs/1204.5221 and is a continuation of the previous question Symmetries in Wilsonian RG
In the liked paper why do the equalities in equation ...
6
votes
0answers
89 views
Dimensional regularization and IR divergences and scale invariance
I want to know if dimensional regularization has any issues if the theory has IR divergences or is scale invariant.
Does dimensional regularization see "all" kinds of divergences?
I mean - what ...
9
votes
1answer
272 views
Symmetries in Wilsonian RG
I wanted to know if there is a theorem that in writing a Lagrangian if one missed out a term which preserves the (Lie?) symmetry of the other terms and is also marginal then that will necessarily be ...
6
votes
0answers
154 views
Regulator-scheme-independence in QFT
Are there general conditions (preservation of symmetries for example) under which after regularization and renormalization in a given renormalizable QFT, results obtained for physical quantities are ...
4
votes
1answer
102 views
Soft Mass and Physical Mass in Softly-broken SUSY
In softly broken SUSY, the bare mass parameters may be specified at e.g. the GUT scale, and then we can run these down to another scale using RGEs, similar in form to the RGEs for gauge couplings, ...
3
votes
0answers
123 views
Zeta regularization gone bad
This may sound as a mathematical question, but it should be very familiar to physicists. I am trying to perform an expansion of the function $$f(x) = \sum_{n=1}^{\infty} \frac{K_2(nx)}{n^2 x^2},$$ for ...
1
vote
1answer
153 views
Renormalization: Why is only a finite number of counter-terms allowed?
I have a question please about renormalization in QFT. Why a renormalizable theory requires only a finite number of counter-terms?
1
vote
2answers
99 views
Can't find the mass scale; calculation using the modified minimal subtraction scheme and dimensional regularisation
I am taking a course on quantum field theory where there is some confusion regarding the renormalisation scheme we are using (and a corresponding one in my mind). Apparently the lecturer meant MS-bar ...
10
votes
1answer
203 views
Why do irrelevant operators require infinitely many counterterms?
As far as I understand it, in the Wilsonian picture of renormalization, we view a theory as having some fixed cutoff and bare couplings, and integrate out high-momentum modes to understand what ...
8
votes
1answer
161 views
Can modern twistor methods to calculate scattering amplitudes be applied to renormalization group calculations?
As explained for example in this article by Prof. Strassler, modern twistor methods to calculate scattering amplitudes have already been proven immensely helpful to calculate the standard model ...
4
votes
0answers
105 views
Does the Standard Model have a Landau pole?
I have seen the statement that the Standard Model has a Landau pole, or at least it its believed that it does at $\sim 10^{34}$ GeV. Has this actually been proven (at least in perturbation theory, as ...
1
vote
3answers
111 views
Effective operator in four-fermion interaction
In one book, I have got the following lines which I found myself unable to understand what is effective operator? The paragraph is given below:
The weak interaction describes nuclear beta decay, ...
4
votes
1answer
78 views
Dimensional transmutation in Gross-Neveu vs others
Firstly I don't know how generic is dimensional transmutation and if it has any general model independent definition.
Is dimensional transmutation in Gross-Neveau somehow fundamentally different ...
4
votes
1answer
175 views
Defining a CFT using beta-functions
Won't it be correct to define a CFT as a QFT such that the beta-function of all the couplings vanish?
But couldn't it be possible that the beta-function of a dimensionful coupling vanishes but it ...
4
votes
0answers
94 views
Confused by renormalization [duplicate]
Possible Duplicate:
Suggested reading for renormalization (not only in QFT)
I'm trying to learn QFT. I don't quite understand why renormalization works. If you are calculating a Feynman ...
3
votes
1answer
123 views
Nonpertubative renormalization in quantum field theory versus statistical physics
I am trying to work my head around how renormalization works for quantum field theory. Most treatments cover perturbative renormalization theory and I am fine with this approach. But it is not the ...
1
vote
1answer
110 views
Divergence in Supergravity
I'm not familiar with supergravity so here's my question: I've heard in talks that if one finds divergence for five-loop 4-graviton scattering amplitudes in five dimensions this translates to a ...
4
votes
0answers
56 views
Are irrelevant terms in the Kahler potential always irrelevant, even at strong coupling?
I've been reading about the duality cascade in Strassler's TASI '03 lectures (hep-th/0505153). He reminds us of the non-renormalization theorem theorem for the superpotential so that the beta ...
6
votes
0answers
194 views
Renormalization group evolution equations and ill-posed problems
There is a class of observables in QFT (event shapes, parton density
functions, light-cone distribution amplitudes) whose the renormalization-group
(RG) evolution takes the form of an ...
4
votes
2answers
201 views
What's the difference between divergences that can be corrected and those that can't
I'm confused by renormalization . If a lagrangian has a term with negative mass dimension , why can't the divergences be absorbed into lagrangian coefficients? What's the difference between ...
4
votes
1answer
110 views
$U(1)$ beta function of low energy effective Seiberg-Witten theory
My question is about figure3 (page 8) of this paper
hep-th/9705131.
Start from Seiberg-Witten theory, integrate out the charged
high energy modes down to Higgs scale and we get a $U(1)$ gauge
theory ...
5
votes
2answers
226 views
Can scattering amplitudes be simplified with 1PI diagrams?
I have been teaching myself quantum field theory, and need a little help connecting different pieces together. Specifically, I'm rather unsure how to tie in renormalization, functional methods, and ...
5
votes
1answer
208 views
Residues in QFT propagator
It is a well known fact that the location of the pole of a propagator (in QFT) can be interpreted as the physical mass.
Is there an interpretation for the residue of the propagator?
Note: I´m ...
3
votes
0answers
41 views
Linear combination of anomalous dimensions in effective potential on pseudomoduli space
In the paper of Intriligator, Seiberg, and Shih from 2007, they give an expression for the effective potential on the pseudo-moduli space $X$, estimated at large $X$ (equation 1.3).
In this equation, ...
5
votes
2answers
240 views
Quantum field theories with asymptotic freedom
QCD is the best-known example of theories with negtive beta function, i.e., coupling constant decreases when increasing energy scale. I have two questions about it:
(1) Are there other theories with ...
2
votes
1answer
162 views
Is proper time renormalization gauge invariant?
Proper Time Renormalization is achieved by putting:
$$ \int_0^\infty e^{iat} dt = {1\over ia} $$
Is it true that this is the only kind of normalization that is gauge invariant? If so, why do famous ...
13
votes
1answer
414 views
Multi-loop beta function of gauge theory (*without* Feynman diagrams)
I would like to point to the beautiful section 4.3 (page 42) of these lecture notes. I think this is the most educative exposition I have ever seen anywhere about Yang-Mill's beta function. What I ...
3
votes
2answers
192 views
What is the exact relationship between scale invariance and renormalizability of a theory?
I have often read that renormalizability and scale invariance are somehow related. For example in this tutorial on page 12 in the first sentence of point (7), self similarity (= scale invariance ?) is ...
6
votes
1answer
164 views
Renormalization of field strength
I'm revisiting the elementary algorithms of renormalization that are taught in a classroom setting and find that the procedure taught to students is as follows:
Write down the bare Lagrangian: ...
1
vote
0answers
105 views
Why does renormalization need an unbroken symmetry?
Common wisdom is that for a QFT to be renormalizable it must be invariant under a symmetry transformation. Why does renormalization need an unbroken symmetry? Which is the first publication that ...
1
vote
0answers
60 views
Wilsonian vs 1PI
As a follow up to Difference between 1PI effective action and Wilsonian effective action, where can I find pedagogical material that highlights the similarities and differences between the 1PI and ...
