Questions tagged [non-perturbative]

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

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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}} \...
Andrew McAddams's user avatar
8 votes
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211 views

QFT's bound states references

At a graduate level, QFT courses teach very well how to perform perturbative calculations using LSZ or even the background field method. Plenty of books are suggested to go into the details of this ...
8 votes
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177 views

Question about the vacua of the Standard Model

This question is probably based on a misunderstanding. Please correct me if I'm wrong, and if unclear, I'll try to put it in a clearer language. In Yang-Mills theory such as the theory of strong ...
SRS's user avatar
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7 votes
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Kallen-Lehmann representation and branch cuts at threshold masses

Let us consider the Kallen-Lehmann representation for the two-point function of scalar fields $$ \langle \Omega | T\left\{\phi(x) \phi(y)\right\}|\Omega\rangle = \int \frac{d^4 p}{(2\pi)^4} e^{ip\...
apt45's user avatar
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Higher category theory, renormalization, and non-perturbative QFTs

I'm (vaguely) aware of certain uses of higher category theory in attempts to mathematically understand quantum field theories -- for example, Lurie's work on eTQFTs, the recent-ish book by Paugam, and ...
6 votes
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2D CFT from sigma models

$X$ is a closed manifold with a positive-definite metric $g$. $M_2$ is a 2D oriented closed manifold with a positive-definite metric $G$ and a compatible volume form $\omega$. We can then consider the ...
Leo's user avatar
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6 votes
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Area and perimeter

Apparently (?), a line operator over a very large loop with length $L$ can obey either perimeter law or area law, $-\log\langle U\rangle\sim L^a$ with $a=1,2$, respectively. We call these options &...
AccidentalFourierTransform's user avatar
4 votes
2 answers
401 views

Worldline formalism and QCD

The worldline formalism of QFT (as I understand it) is a first quantisation approach to particle physics. We consider '0+1 dimensional QFT happening on the worldline of the particle' in the same way ...
ColourConfined's user avatar
4 votes
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143 views

Can convergent perturbation series be incorrect for an action linear in the perturbation?

Non-perturbative effects are common in mathematics. For example, consider the function $$f(g) = e^{-1/g}+ g + \frac{1}{10} g^2$$ and suppose this function is the answer to some math problem. ...
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How do we perform a perturbative expansion for magnetic monopoles?

Magnetic monopoles in non-abelian (and even abelian) gauge theory essentially appear as a non-perturbative, composite phenomenon if we perform the standard perturbative expansion in terms of, say, ...
Tevatron5's user avatar
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Renormalization in non-perturbative QFT ($n$-point function)

How does one do renormalization if one can exactly calculate the $n$-point function of QFT? Take for example QED when doing renormalization We calculate $2$ and $3$ point function Expand them in ...
aitfel's user avatar
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What is the problem of non-pertubative quantisation?

In reading books about quantisation, there is (sometimes hidden) the claim, that quantisation is done using a pertubative approach. You look at the free field, find that it is essentially a sum of ...
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Perturbative coupling for QFT

I'm confused about the definition of a perturbative coupling for QFT that it should be less than 4 $\pi$, because the higher order corrections comes of order $\lambda/(4 \pi)$ .. Now why QCD is not ...
S.S.'s user avatar
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Non-perturbative approach to QFT in Hamiltonian formalism?

A simple conceptual question today: is it true that QFT can only be approached in a non-perturbative way only through the functional methods (like 1/N), while in the Hamiltonian formalism we can only ...
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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 \...
Name YYY's user avatar
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4 votes
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132 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^{\...
Name YYY's user avatar
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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 ...
dan-ros's user avatar
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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 ...
Angie38750's user avatar
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163 views

Witten anomaly and bound states of fermions

In his famous paper "An SU(2) anomaly", Witten begins by noting that an SU(2) gauge theory with a single fermion in the doublet representation is weird, since there is "no obvious ...
AccidentalFourierTransform's user avatar
3 votes
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Physical consequences of Gribov ambiguities in semiclassical theories

Gauge theories in the pathintegral formalism are plagued by so called Gribov ambiguities. If one picks some gauge, by defining it via $F[A]=0$, then it is generally the case, that the hypersurfaces ...
Question Asker's user avatar
3 votes
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235 views

Why is the chiral condensate a negative quantity?

The chiral condensate serves as an order parameter for the chiral phase transition. Thus, it is a finite quantity in one phase and vanishes in the other phase. It is given as a vacuum expectation ...
Bernd's user avatar
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254 views

Do sum rules for spectral function always hold?

In condensed matter physics, we can define the spectral function as $$ A_{\alpha}(\omega) = -\frac{1}{\pi}\mathrm{Im}G_{\alpha}^R (\omega) $$ It can be shown that this quantity satisfies the sum rule: ...
RedGiant's user avatar
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Is it possible to treat fermion reheating from inflaton decay only perturbatively?

In case of an inflaton Lagrangian $ \mathcal{L} = \frac{1}{2} (\partial_\mu \phi)^2 - \frac{1}{2}m_\phi^2 \phi^2 -h \overline{\psi} \phi \psi $ where the inflaton field is coupled only to fermions ...
Cristina Benso's user avatar
3 votes
0 answers
118 views

Are Green functions non-perturbatively infrared finite?

Are Green functions non-perturbatively infrared finite? In other words imagine one had the final form of the 4-point function for spin-1/2 field, do we still need infrared radiation correction? In ...
Bastam Tajik's user avatar
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3 votes
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What would a non-perturbative renormalization group treatment for polymers look like?

I know that one can do perturbative renormalization for the polymer excluded volume problem or the self-avoiding walk problem corresponding to n=0 component field theory. Here in Hamiltonian, we have, ...
noisyoscillator's user avatar
3 votes
0 answers
241 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 ...
user47299's user avatar
  • 301
3 votes
0 answers
377 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 ...
Stan's user avatar
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2 votes
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Double-well potential and non-perturbative energy splitting

(A reference for the topic is a QFT note (chapter 2 Instantons in Quantum Mechanics) here by Yoichi Kazama at University of Tokyo, see page 30) Consider the double well potential in quantum mechanics, ...
user31415926's user avatar
2 votes
0 answers
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Interacting QFTs and Virtual Particles

Short introduction to my understanding: As far as i understand, virtual particles are usually defined to be the internal lines in Feynman Diagrams. But we know that those are just useful tools to ...
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2 votes
1 answer
96 views

General matrix element of electromagnetic current between states of different masses?

Weinberg (Chapter 10, problem 3) in Quantum Theory of Fields Volume 1 asks for the matrix element: $$\langle {\mathbf{p}_2\sigma_2}|{J^{\mu}(x)}|{\mathbf{p}_1\sigma}\rangle $$ of the electromagnetic ...
physicsbootcamp's user avatar
2 votes
0 answers
43 views

$SU(2)$ gauge SUSY with Affleck-Dine-Seiberg term

Consider SUSY gauge theory with $SU(2)$ group and matter fields $Q$ and $\bar{Q}$ in fundamental and anti-fundamental representations correspondently and the following superpotential: $$W=\frac{{\...
DGeometry's user avatar
2 votes
0 answers
161 views

QCD generating functional and QCD vacuum from nonperturbative to perturbative regime!

The complete generating functional in QCD (starting from the most general renormalizable, Lorentz invariant and gauge invariant Lagrangian) given by $$Z_\theta[J]=\int \mathcal{D}A \exp i\int d^4x~ {\...
SRS's user avatar
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2 votes
0 answers
214 views

Implications of Instanton Corrections (to Degenerate Vacuua) for Spontaneous Symmetry Breaking

We consider that if the classical vacuua of a theory are degenerate then each of them can be non-invariant under one or more of the symmetries of the Lagrangian. We can choose one of the vacuua and ...
user avatar
2 votes
0 answers
100 views

The role of the renormalization scale in the functional renormalization group

On p. 28 of Bertrand Delamotte's Introduction to the Nonperturbative Renormalization Group he writes $k$ [the renormalization scale] acts as an infrared regulator (for $k \neq 0$) somewhat similar ...
Janosh's user avatar
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2 votes
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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 (...
Thomas's user avatar
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2 votes
0 answers
40 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 (...
Name YYY's user avatar
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2 votes
0 answers
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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 {...
Andrew McAddams's user avatar
2 votes
0 answers
290 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 ...
user avatar
1 vote
0 answers
36 views

Can all classical optical materials be described by perturbation theory?

In quantum field theory (e.g. lattice QED), perturbation theory can "break down" when interactions become too strong. Can something like that happen in classical non-linear optics? Can there ...
Adomas Baliuka's user avatar
1 vote
0 answers
36 views

Why is it justified to focus on gauge transformations constant at spatial infinity in QCD instantons?

In the context of Yang-Mills theories and QCD instantons, much of the literature and conventional treatment hinges on the consideration of gauge transformations that remain constant at spatial ...
Kris's user avatar
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1 vote
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Is QCD parity conserving also non-perturbatively?

Since QCD is fundamentally non-perturbative at low energies one may ask if QCD is still Parity conserving. In the path-integral formalism using the Faddeev–Popov ghosts as gauge fixing terms the ...
krabby patty's user avatar
1 vote
0 answers
59 views

Do Universal Spacetimes have Non-perturbative quantum corrections?

Universal spacetimes have the interesting property that their quantum corrections vanish to all loop orders, and can be viewed as classical solutions to speculative theories of quantum gravity like ...
CuriousDroid's user avatar
1 vote
0 answers
61 views

$SU(2)$ gauge supersymmetric theory and superpotential

I am currently studying supersymmetry and I came across a superpotential of the following form $$W=\frac{\Lambda^5}{\bar{Q}Q}+m\bar{Q}Q.$$ The first term is said to appear as a result of non-...
DGeometry's user avatar
1 vote
1 answer
192 views

Relation Asymptotic Series and perturbative effects

Perturbative expansions of a function $f(x)$ around say $x=0$ cannot determine contributions from a function such as $e^{-1/x}$ since its Taylor series vanishes to all orders. This kind of ...
Kvothe's user avatar
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1 vote
0 answers
56 views

Perturbative series in physics: why are coeffcieints of Gevrey-1 type (i.e. bounded by $\alpha C^n(n!)^1$

I have only been able to find this explicitly mentioned in this paper on resurgence techniques in physics. And have chased up the hints it gives, but they are not very explanatory. Essentially, the ...
Meep's user avatar
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1 vote
0 answers
140 views

What is the difference between real and complex instantons (mathemtically, and their physical significance), and connection to Wick rotation

I am struggling to understand the difference and physical significance between real and complex instantons- I think these are also sometimes called ghost instantons? There are also anti-instantons. ...
Meep's user avatar
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1 vote
0 answers
131 views

Nonperturbative results for $\phi^3$ theory in dimensions $d>6$?

The theory is nonrenormalizeable in those dimensions, but can you say anything about the theory anyway? Specifically I am wondering about the status of whether the theory is trivial, i.e. a ...
fewfew4's user avatar
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0 answers
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Change of scaling due to a perturbation

I am looking for known examples of models where the introduction of a perturbation changes the scaling law of one or more observables. I would appreciate suggestions relevant to any branch of Physics, ...
AndreaPaco's user avatar
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0 votes
0 answers
126 views

Is the $S$-Matrix analytic in Planck constant?

Taking the scattering amplitude as a function of $\hbar$, is such function necessarily analytic in this variable. Suppose I'm concerned with Relativistic Quantum Field Theory. In QED, the tree level ...
Bastam Tajik's user avatar
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Can the Functional Renormalization Group not generate a flow that is generated perturbatively?

I think I might have stumbled on a calculation that appears to undergo renormalization when you compute it perturbatively, but not when you compute it using the FRG. Consider, for the sake of argument,...
Níckolas Alves's user avatar