Use this for questions which discuss models of quantum theories which do not make use of peturbation theory.

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1answer
37 views

Experimental observation of non-perturbative effects

Many quantum field theories come with non-perturbative objects such as solitons and instantons, and non-perturbative effects such as the Schwinger effect. However, it is hard to find any review on ...
3
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1answer
35 views

Is CP problem the problem?

I've heard an argument that the question of smallness of QCD $\theta$ parameter is called the problem (namely, strong CP problem), since the other dimensionless couplings (like $\alpha_{s}$), are of ...
5
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2answers
56 views

Why cannot a fundamental string couple to the R-R gauge field $C_{\mu\nu}$?

People usually say that D-branes can carry R-R charges, or can couple to R-R sector gauge fields. But why a fundamental string cannot couple to a 2-form R-R sector gauge field? What's the essential ...
3
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0answers
42 views

Some questions about QCD [closed]

About QCD, I have two questions. I know I should propose one question one time, but they are actually two steps of the same question: Non-perturbative aspects of QCD. 1, Why do we need to solve QCD ...
5
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2answers
84 views

Why are CFT descriptions of String Theory inherently perturbative and how can it be circumvented?

Field theories like QED/QCD are a priori non-perturbative theories. Perturbatively you can describe them by Feynman diagrams which essentially sum over all topologies of virtual particle creation and ...
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0answers
31 views

Electroweak instanton calculations

Consider an electroweak instanton in a model beyond the Standard Model with explicit baryon plus lepton number ($B+L$) violation. This instanton decays into nine quarks $q$ and three leptons $l$, ...
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0answers
26 views

Does an instanton couple equally to all flavors?

Do gravitational / electroweak / QCD / ... instantons couple equally to all fermion flavors? For example, do QCD instantons distinguish between the different quark flavors? Edit, due to comment (...
3
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1answer
53 views

Nonperturbative corrections that can break SUSY

I am puzzled by a statement that is made regarding non-perturbative corrections breaking supersymmetry. Specifically, consider a one-dimensional system, described by the Hamiltonian $$H = \frac{1}{2}...
1
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1answer
42 views

Non-perturbative Brane effects

In Johnson's Book about D-branes he gets the Tension of a D brane: $$\tau_p = \frac{\sqrt{\pi}}{16 \kappa_0 g_s}(4\pi^2\alpha')^{(11-p)/2}$$ By performing a string amplitude calculation and ...
2
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1answer
93 views

How do we calculate the S-matrix using non-perturbative QFT?

The cross section of a scattering process in $QFT$ is computed in terms of the S-matrix elements. In perturbative $QFT$, the same is done by computing the S-matrix elements by using Feynman ...
2
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1answer
85 views

Baryon number violation in the Standard Model

Anomaly cancellation in the Standard model requires $B-L$ to be constant, which is done using perturbative diagrammatic expansion. Secondly, baryon number is conserved as an $U(1)$ global field ...
3
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0answers
40 views

Topological terms VEVs and ghosts

Suppose we have the Standard model, and we want to calculate with VEVs of topological susceptibilities of $SU_{L}(2), U_{Y}(1)$ and $SU_{c}(3)$ fields, which have the form $$ \tag 1 \kappa \equiv \...
2
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2answers
165 views

What are non-perturbative effects and how do we handle them?

Schwartz's QFT book contains the following passage. To be precise, total derivatives do not contribute to matrix elements in perturbation theory. The term $$\epsilon^{\mu\nu\alpha\beta} F_{\mu\...
3
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1answer
40 views

Continuum of lattice QCD is free?

I am having a hard time getting to grips with the statement that $$g_{0}(a) \to 0 \text{ as } a \to 0$$ where $g_{0}$ is the bare coupling in lattice QCD and $a$ the lattice spacing. How come this ...
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0answers
28 views

The question about codimension of fixed point and about irrelevant operators

Recently I've read about Wilsonian renormalization group (WRG) in context of condensed matter phase transitions. The important concepts of WRG are fixed points and type of operators (eigenvalue, ...
1
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1answer
21 views

B and L violation by non-perturbative electroweak effects

I was reading about the definition of R-parity on this paper http://arxiv.org/abs/hep-ph/9709356 (pg. 53 54). The author says that postulating B and L numbers conservation in the MSSM is sub-optimal ...
3
votes
2answers
449 views

Why are many physicists trying to develop non-perturbative quantum theories? [closed]

I would like to briefly know where (and why) does perturbation theory fail and why are physicists so desperate looking for non-perturbative theories.
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0answers
24 views

Green function of squared chiral pseudoscalar in QCD

I need to compute the Green function $$ G(0) \equiv \int d^{4} x\int D[\text{QCD}]\bar{q}\gamma_{5}Mq(x)\bar{q}M\gamma_{5}q(0)e^{iS_{QCD}} \equiv $$ $$ \tag 1 \equiv \int d^{4}x\langle 0|T( \bar{q}\...
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0answers
34 views

Topological susceptibility of electroweak theta-term

Suppose EW theory generating functional: $$ Z[\text{sources}] = \int D(A,\psi,\bar{\psi}, H,H^{\dagger})\text{exp}\bigg[i\int d^{4}x\bigg(-\frac{1}{4g_{EW}^2}F_{EW}^2 + \bar{\psi}(D - m)\psi + DH^{\...
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0answers
91 views

Physical meaning of Ward Identity and computing vertex functions

Following the derivation of Ward Identity by Weinberg book, you get it in the form $$ (l-k)_\mu S'(k)\Gamma^\mu(k,l)S'(l) = i S'(l) - iS'(k) $$ Can anyone explain the physical meaning of this ...
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1answer
162 views

Mathematical proof that $\exp(-1/|g|)$ is always related with formation of bound states through scales?

I know that this function ($g$ means coupling) is non-analytical in $g=0$, so this function is only appreciable under non-perturbative calculations, so is a non-perturbative phenomena. This function ...
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0answers
115 views

How do instantons look in real time/spacetime?

Instantons, as I understand it, are mathematical constructions in Eucledean spacetime. Does it imply that instantons do not exist in real spacetime or instanton tunneling effects are does not have ...
2
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1answer
111 views

complicated QCD Color factor formula?

I was doing higher order calculations for purely gluonic system and came across complicated color factors like the product of six structure constants product $f_{a_1a_2a_3}f_{a_4a_2a_7}f_{a_7a_8a_1}f_{...
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0answers
38 views

Bound states and corresponding elementary fields

Let's have some bound state, like positronium or meson. I need to calculate an amplitude of process which involves bound state in in- or out-state. Is it necessary to introduce corresponding ...
3
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0answers
107 views

Why is QCD hard to solve if I know the beta functions?

Why is it still hard to solve QCD if we know the beta functions of the coupling? Aren't only the loops causing problems? And am I not able to write every possible interaction exact at tree-level with ...
1
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1answer
33 views

Translational versus dilatational zero modes?

Why are the zero modes of the SU(2) Yang Mills instanton referred to as translational or dilatational zero modes? Is this standard terminology?
2
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0answers
23 views

Decay of some particle involved quarks vs mesons as outgoing states

Let's have decay width of some mother particle into the state which involves hadrons. For simplicity, let's assume that creation of hadrons (on diagram) is possible only through electroweak vertices (...
0
votes
1answer
297 views

difference between classical vacuum solutions and instantons

What does the classical vacuum of the $SU(2)$ Yang-Mills action correspond to? Does it correspond to $F_{\mu\nu}=0$ everywhere or just at the spatial infinity? In Srednicki’s book, he has shown that, ...
8
votes
1answer
201 views

Do we need new physics to supercede triviality?

I've been reading about the higgs triviality bound (see for example here). It is discussed that the higgs self coupling at some energy scale becomes non-perturbative. If the higg's mass is above about ...
5
votes
1answer
209 views

Non-Perturbative feynman diagrams?

The wikipedia page for Feynman Diagrams claims that Thinking of Feynman diagrams as a perturbation series, nonperturbative effects like tunneling do not show up, because any effect that goes to ...
1
vote
1answer
142 views

Rewriting the Hydrogen Schrodinger Equation as a system of differential equations

I have only ever seen the Schrodinger equation for the hydrogen atom written out in a form like this: $$ -\frac{\hbar^2}{2\mu}\left[\frac{1}{r^2}\frac{\partial}{\partial r}\left(r^2\frac{\partial \psi}...
3
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1answer
132 views

Significance of total divergence anomaly term

What is the significance of the fact that the anomany term (calculated from the triangle diagram) is a total divergence? Or, in other words, what is the significance of $$\partial_\mu j^\mu_A\sim Tr(W\...
2
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0answers
45 views

Theory with interaction and the birth of bound states during propagation

Suppose we want to calculate vacuum expectation $$ \tag 1 D_{lm}(x - y) = \langle \Omega | \hat {T}\left( \hat {\Psi}_{l}(x)\hat {\Psi}_{m}^{\dagger}(y)\right)| \Omega\rangle = \langle \Omega| \hat {...
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0answers
156 views

One more time about LSZ-theorem

This question is the continuation of this one. For simplicity, let's use $(1)$ from the linked question (it is called n-point Green function and in particle case coincides with internal diagram), $$ ...
3
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0answers
617 views

LSZ reduction theorem derivation in Weinberg QFT

When deriving LSZ reduction theorem Weinberg in his QFT book have assumed n-point generalized Green functions, $$ G(q_{1},...,q_{n}) = \int d^{4}x_{1}...d^{4}x_{n}e^{-i\prod_{i =1}^{n}q_{j}x_{j}} \...
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0answers
127 views

Perturbative vs. non-perturbative approaches to a well-defined Yang-Mills theory in 4 dimensions

Another question regarding the Yang-Mills Existence and Mass Gap problem (http://www.claymath.org/sites/default/files/yangmills.pdf). Does the problem require that the "construction" of a four ...
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0answers
204 views

Definition of a non-pertubative Quantum field theory

How do you define a non-perturbative Quantum field theory. What does it mean? I was just digging around some math about the meaning of $Z_1$, and such in terms of probabilities. It turns out these and ...
4
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58 views

Mirrored decoupling fermion doublers and a lattice chiral fermion / gauge theory

Nielsen Ninomiya Fermion-doubling problem has known to be a challenge to construct a chiral fermion or chiral gauge theory on the lattice. There is a proposed resolution to use so-called two mirrored ...
5
votes
1answer
178 views

Separation of perturbative and non-perturbative contributions in partition function computation

The following is defined, where $\epsilon \to 0^+$ is a cutoff: $$ \mathcal{F}(Z)=\int_{\epsilon}^\infty \frac{\mathrm{d}s}{s} \frac{1}{\sinh^2 s/2} e^{-sx}. $$ Question: how do we see that $\mathcal{...
13
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1answer
646 views

The Origins of Instantons from Path Integrals

I know that you can come across non-perturbative effects in QFT, particular when the coupling constant lies outside the radius of convergence of the asympototic perturbation series. From the ...
3
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0answers
173 views

Why does global supersymmetry commute with gauge transformations?

In particular, I would like to understand the following quotation from a paper by Witten: Nucl.Phys. B188 (1981) 513 (p. 515 at the top) His statement: This is so because in global supersymmetry ...
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242 views

What happens to the amplituhedron in a non-peturbative context?

The Amplituhedron has recently been popular; it supposedly encodes perturbative scattering amplitudes in a simple, geometric fashion. What happens to it in a non-perturbative context? Is there ...
6
votes
2answers
915 views

QCD in the non-perturbative regime

In the list of unsolved problems in physics. Confinement: the equations of QCD remain unsolved at energy scales relevant for describing atomic nuclei. How does QCD give rise to the physics of nuclei ...
4
votes
1answer
72 views

Solitonic nature of RR sources

In the famous paper by Polchinski where he shows that D-branes are sourcing RR fields, he says (before we known the result) that RR sources must be objects with tension going like $1/g_s$ (page two of ...
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2answers
174 views

What constitutes a 'reliable' instanton calculation?

In Modern Supersymmetry, John Terning, on pgs 151, and 153 performs a so called 'reliable' instanton calculation when dealing with the ADS superpotential 'since the gauge group is completely broken'. ...
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4answers
546 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 ...
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1answer
2k views

What's the relation between perturbative and nonperturbative QFT?

In case of any miscommunication let me describe my understanding of the meaning of "perturbative" and "non-perturbative", and correct me if something is wrong: In a perturbatively defined QFT the ...
6
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2answers
1k views

What does a non-perturbative theory mean?

I'm a science writer and I'm having difficulty understanding what a non-perturbative approach means. I thought I understood what perturbative meant, but in looking for explanations of non-perturbative,...
18
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1answer
957 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 ...
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3answers
707 views

How do we know that nonperturbative canonical quantum gravity is wrong?

In these forums and elsewhere it is routinely agreed that "we do not have a theory of quantum gravity." My question is, how do we know that canonical quantum gravity is "wrong"? I understand that the ...