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8
votes
1answer
466 views

Dimensional regularization: removing more than just logarithmic divergencies?

I have followed two courses on QFT, which both involved renormalization by dimensional regularization. My confusion is that one of the professors claimed that dimensional regularization can only be ...
4
votes
1answer
787 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 ...
7
votes
2answers
255 views

On the Axial Anomaly

I know that if we start with a massive theory, the chiral states $L$ and $R$ remain coupled to each other in the massless limit. Because a charged Dirac particle of a given helicity can make a ...
5
votes
1answer
305 views

What does it mean to renormalize an effective field theory?

This is in reference to slide 19 of this talk "As always in Effective Field Theory, the theory becomes predictive when there are more observables than parameters" Can one explain what this exactly ...
2
votes
1answer
89 views

Are these IR and UV divergences equal [closed]

let be 2 divergent integrals $$ \int_{0}^{\infty}\frac{p^{3}dp}{(p^{2}+m^{2})^{2}}= A $$ $$ \int_{0}^{\infty}\frac{dp}{p(p+q)^{2}}=B $$ B has a divergent as $ p \to 0 $ however i can use a change ...
0
votes
0answers
196 views

$\mathrm{i}\epsilon$ prescription makes a function analytical?

I've seen this everywhere where they say "Analytic continuation is obtained by the usual $\mathrm{i}\epsilon$ prescription..." but how is that? How do you analytically continue (say) $\ln x$ with ...
3
votes
1answer
646 views

Critical Dimension of Bosonic Strings and Regularization of $\sum_{n=1}^\infty n$

If $D$ is critical dimension of Bosonic strings, a particular derivation goes like the following, where we arrive finally at $$ \frac{D-2}{2}\sum_{n=1}^\infty n + 1 = 0. $$ Now mathematically this is ...
2
votes
1answer
230 views

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 ...
1
vote
1answer
113 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
74 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 ...
4
votes
1answer
156 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 ...
5
votes
2answers
289 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 ...
1
vote
0answers
42 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 ...
7
votes
0answers
226 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 ...
5
votes
1answer
257 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 ...
10
votes
1answer
343 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 ...
13
votes
1answer
532 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 ...
6
votes
1answer
215 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 ...
4
votes
0answers
112 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 ...
2
votes
2answers
157 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 ...
5
votes
3answers
4k views

Don't understand the integral over the square of the Dirac delta function

In Griffiths' Intro to QM [1] he gives the eigenfunctions of the Hermitian operator $\hat{x}=x$ as being $$g_{\lambda}\left(x\right)~=~B_{\lambda}\delta\left(x-\lambda\right)$$ (cf. last formula on ...
2
votes
0answers
89 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 ...
3
votes
2answers
258 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 ...
8
votes
2answers
397 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 ...
2
votes
0answers
111 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
163 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 ...
2
votes
0answers
209 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 ...
9
votes
1answer
300 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 ...
3
votes
1answer
845 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 ...
6
votes
1answer
203 views

Two-loop regularization

Working out some quantum field theory computations, I have to find out the value of the two-loop Feynman integral $$ ...
0
votes
1answer
98 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 ...
2
votes
4answers
355 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 ...
22
votes
2answers
2k 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 ...
3
votes
2answers
487 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 ...
3
votes
1answer
564 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 ...
9
votes
0answers
272 views

Gauge invariant but not gauge covariant regularization

I'm not sure if someone's already asked this before, but I was wondering, in field theory, when we say that a certain field is gauge invariant but not gauge covariant, what does this mean? In ...
3
votes
2answers
434 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 ...
12
votes
1answer
463 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 ...
2
votes
0answers
153 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} ...
3
votes
2answers
331 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
0answers
259 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 ...
8
votes
2answers
566 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 ...
20
votes
3answers
553 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 ...
5
votes
2answers
250 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
2answers
588 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 ...
8
votes
7answers
632 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 ...
3
votes
1answer
149 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} = - ...
6
votes
4answers
835 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 ...
13
votes
5answers
247 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 ...
3
votes
2answers
381 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 ...