The regularization tag has no wiki summary.
21
votes
13answers
2k views
Suggested reading for renormalization (not only in QFT)
What papers/books/reviews can you suggest to learn what renormalization "really" is? Standard QFT textbooks are usually computation-heavy and provide little physical insight in this respect - after my ...
16
votes
3answers
143 views
Regularization of the Casimir effect
For starters, let me say that although the Casimir effect is standard textbook stuff, the only QFT textbook I have in reach is Weinberg and he doesn't discuss it. So the only source I currently have ...
13
votes
5answers
131 views
Other processes than formal power series expansions in quantum field theory calculations
I am not sure if this question is too naive for this site, but here it goes. In QFT calculations, it seems that everything is rooted in formal power series expansions, i.e. , what dynamical systems ...
13
votes
1answer
600 views
Classical and quantum anomalies
I have read about anomalies in different contexts and ways. I would like to read an explanation that unified all these statements or point-views:
Anomalies are due to the fact that quantum field ...
13
votes
3answers
517 views
Does renormalization make quantum fields into (slightly) nonlinear functionals of test functions?
Quantum fields are presented as operator-valued distributions, so that the operators in the theory are linear functionals of some test function space. This works well for free fields, giving us a ...
9
votes
1answer
218 views
Instantons, anomalies, and 1-loop effects
A symmetry is anomalous when the path-integral measure does not respect it. One way this manifests itself is in the inability to regularize certain diagrams containing fermion loops in a way ...
9
votes
2answers
573 views
Are there books on Regularization and Renormalization in QFT at an Introductory level?
Are there books on Regularization and Renormalization, in the context of quantum field theory at an Introductory level? Could you suggest one?
Added: I posted at math.SE the question Reference ...
9
votes
1answer
262 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 ...
8
votes
1answer
463 views
Iterated dimensional regularization
Given a 2-loop divergent integral $\int F(q,p)\,\mathrm{d}p\mathrm{d}q$, can it be solved iteratively? I mean
I integrate over $p$ keeping $q$ constant
Then I integrate over $q$
In both iterated ...
8
votes
2answers
500 views
Regularisation of infinite-dimensional determinants
Can a regularisation of the determinant be used to find the eigenvalues of the Hamiltonian in the normal infinite dimensional setting of QM?
Edit: I failed to make myself clear. In finite ...
7
votes
7answers
389 views
Why regularization?
In quantum field theory when dealing with divergent integrals, particularly in calculating corrections to scattering amplitudes, what is often done to render the integrals convergent is to add a ...
6
votes
2answers
148 views
Is the step of analytic continuation unavoidable or can you model around it?
One sometimes considers the analytic continuation of certain quantities in physics and take them seriously. More so than the direct or actual values actually. For example if you use the procedure for ...
6
votes
4answers
563 views
Is QFT mathematically self-consistent?
After recently going through a short program of self-study in quantum mechanics, I was surprised to find a quote attributed to Feynman essentially saying he was extremely bothered by the computational ...
6
votes
1answer
203 views
Does string theory provide a physical regulator for Standard Model divergencies?
In other question, Ron Maimon says that he thinks string theory is the physical regulator. I did not know that string theory regularize divergencies.
So, Q1: How does string theory regularize the ...
6
votes
0answers
80 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 ...
6
votes
0answers
150 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 ...
5
votes
6answers
763 views
Laplacian of $1/r^2$ (context: electromagnetism and poisson equation)
We know that a point charge $q$ located at the origin $r=0$ produces a potential $\sim \frac{q}{r}$, and this is consistent with the fact that the Laplacian of $\frac{q}{r}$ is
...
5
votes
2answers
1k views
Limit of Lorentzian is Dirac Delta
I have a quick question that just came up in my research and I could not find an answer anywhere so I thought I'd try here.
So one of the definitions of the Dirac Delta is the limit of the Lorentzian ...
5
votes
1answer
139 views
Two-loop regularization
Working out some quantum field theory computations, I have to find out the value of the two-loop Feynman integral
$$
...
5
votes
2answers
172 views
Dimensional Regularization Integral Formula
In the formula $$\int \frac {d^{4-2\epsilon} l} {(2\pi)^{4-2\epsilon}} \frac 1 {(l^2-\Delta)^2} = \frac i {(4\pi)^{2-\epsilon}} \Gamma(\epsilon) \left(\frac 1 \Delta\right)^\epsilon,$$ how should I ...
4
votes
3answers
712 views
Don't understand the integral over the square of the Dirac delta function
In Griffiths' Introduction to Quantum Mechanics he gives the eigenfunctions of the Hermitian operator $\hat{x}=x$ as being
$$g_{\lambda}\left(x\right)~=~B_{\lambda}\delta\left(x-\lambda\right).$$
...
4
votes
2answers
392 views
Zeta-function regularization in QFT for heat kernels
When one is doing zeta-function regularization of the heat-kernel for QFT then one is doing these following steps,
the integral over the imaginary time
taking the trace of the heat-kernel or the ...
4
votes
2answers
98 views
Dimensional Regularization involving $\epsilon^{\mu\nu\alpha\beta}$
Is it possible to dimensionally regularize an amplitude which contains the totally antisymmetric Levi-Civita tensor $\epsilon^{\mu\nu\alpha\beta}$?
I don't know if it's possible to define
...
4
votes
0answers
94 views
Confused by renormalization [duplicate]
Possible Duplicate:
Suggested reading for renormalization (not only in QFT)
I'm trying to learn QFT. I don't quite understand why renormalization works. If you are calculating a Feynman ...
3
votes
2answers
214 views
How are functional determinants of Laplace-type operators used in physics?
Many mathematical papers concerning the $\zeta$-regularized Determinant of Laplace-type operators refer for motivation to the broad use of such determinants in mathematical physics, especially in ...
3
votes
1answer
76 views
Pauli-Villars (PV) regularisation breaks supersymmetry. How to see that?
Does the PV regulator breaks SUSY?
Take for instance the 1-loop (top/stop loops) correction to the Higgs squared-mass parameter in the MSSM, and you'll get something like,
$$\delta m^2_{h_u} = - ...
3
votes
1answer
287 views
A certain regularization and renormalization scheme
In a certain lecture of Witten's about some QFT in $1+1$ dimensions, I came across these two statements of regularization and renormalization, which I could not prove,
(1) $\int ^\Lambda \frac{d^2 ...
3
votes
2answers
267 views
Pade Approximant
I have some questions about Pade approximants.
Given a divergent power series $ \sum_{n >0} a(n)x^{n} $ can we use a Pade Approximant to it $ R(x)$ so we can obtain a SUM of the series for every ...
3
votes
1answer
354 views
About calculation of anomalous dimension in Peskin and Schroeder's book.
This question is in reference to question 13.2 in the QFT book by Peskin and Schroeder.
To put it in general - I would like to know how does one define "anomalous dimensions" if one is given the ...
3
votes
0answers
115 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 ...
3
votes
0answers
253 views
Is there a Non-perturbative renormalization algorithm? [duplicate]
Possible Duplicate:
is there non-perturbative RENORMALIZATION ?? if so how it works?
Is there a non-perturbative renormalization algorithm ???, for example to avoid the divergent integrals ...
2
votes
4answers
172 views
Is there a non-perturbative remormalization? If so, how does it work?
Is there a method to renormalize a theory without using perturbative expansions for the divergences? For example, is there a method to get masses and other renormalized quantities without using ...
2
votes
2answers
97 views
Determination of auxiliary scale in dimensional regularization
My questions are in italics. In the article [1] a dimensional regularization is presented on an electrostatic example of an infinite wire with constant linear charge density $\lambda$. It is shown ...
2
votes
2answers
149 views
Gaussian type integral with negative power of variable in integrand
How can we compute the integral $\int_{-\infty}^\infty t^n e^{-t^2/2} dt$ when $n=-1$ or $-2$? It is a problem (1.11) in Prof James Nearing's course Mathematical Tools for Physics. Can a situation ...
2
votes
1answer
298 views
Chiral anomalies à la Fujikawa: Why don't we just take another measure?
When deriving the chiral anomaly in the non perturbative approach for a theory of massless Dirac fermions, you start by showing that the path-integral measure is not invariant unter the chiral ...
2
votes
1answer
94 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 ...
2
votes
0answers
55 views
Cancellation of the quadratic divergence in QCD
I am currently reading about QCD in QFT-Peskin&Schroeder. When calculating 1-loop diagrams for QCD and using dimensional regularization, the 3-vertex boson loop, 4-vertex boson loop and ghost loop ...
2
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0answers
97 views
Regularization of infinite series: an alternative for the not-always-courteous-Zeta
Zeta-function regularization of infinite series is the most commonly used in QFT applications. However, occasionally other schemes are employed which, allegedly, suit the nature (most noticeably the ...
2
votes
0answers
114 views
Functional determinant approximation
Let the Hamiltonian in one dimension be $H+z$, then I would like to evaluate $\det(H+z)$.
I have thought that if I know the function $Z(t) = \sum_{n>0}\exp(-tE_{n})$ I can use
$$\sum_{n} ...
1
vote
2answers
258 views
Is QCD free from all divergences?
On page 8 in http://arxiv.org/pdf/hep-th/9704139v1.pdf David Gross makes the following comment:
"This theory [QCD] has no ultraviolet divergences at all. The local (bare) coupling vanishes, and the ...
1
vote
1answer
72 views
the meaning of epsilon in this operator $ \epsilon $
Consider the dimensional regularized integral
$$ \int d^{d}k (k^{2}-m^{2}+i\epsilon)^{-\lambda} $$
For positive $ \lambda $ this integral has a pole at $ k=m $. Is this the reason we we insert the $ ...
1
vote
1answer
53 views
Casimir force using Pauli-Villars regularization
In Zee's Quantum field theory in a nutshell, 2nd edition, p. 74 he claims that:
$$
\sum_a c_a \Lambda_a \sum_n \frac{\omega_n}{\omega_n + \Lambda_a} = - \sum_a c_a \Lambda_a \sum_n ...
1
vote
0answers
34 views
does this expression appear in renormalization?
my questiion is if this regularizatio for the Harmonic series
$$ \sum_{n=0}^{\infty}\frac{1}{(n+a)} = \frac{ -\Gamma ' (a)}{\Gamma (a)}$$
for any positive and finite 'a' appears in renormalization ...
1
vote
0answers
44 views
Divergent sum in lightcone quantization of bosonic string theory
I had the following question regarding lightcone quantization of bosonic strings - The normal ordering requirement of quantization gives us this infinite sum $\sum_{n=1}^\infty n$. This is regularized ...
1
vote
0answers
61 views
Regulating the sum in Casimir Force
I am trying to evaluate the Casimir force using a Gaussian regulator (I know there are other much easier ways to do this, but I want to try this!) We then are reduced to evaluating the sum
$$ ...
1
vote
0answers
104 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 ...
0
votes
1answer
77 views
mathematical explanation for UV divergences and $ \delta ^{(n)}(0) $
is there any mathematical explanation for the UV divergences ??
i have read that in the framework of Epstein-Glser theory :D these UV divergences appear from the product of distributions
anyone does ...
