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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questions with no upvoted or accepted answers
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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,
$$
G(q_{1},...,q_{n}) = \int d^{4}x_{1}...d^{4}x_{n}e^{-i\prod_{i =1}^{n}q_{j}x_{j}} \...
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QFT's bound states references
At a graduate level, QFT courses teach very well how to perform perturbative calculations using LSZ or even the background field method. Plenty of books are suggested to go into the details of this ...
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Question about the vacua of the Standard Model
This question is probably based on a misunderstanding. Please correct me if I'm wrong, and if unclear, I'll try to put it in a clearer language.
In Yang-Mills theory such as the theory of strong ...
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Kallen-Lehmann representation and branch cuts at threshold masses
Let us consider the Kallen-Lehmann representation for the two-point function of scalar fields
$$
\langle \Omega | T\left\{\phi(x) \phi(y)\right\}|\Omega\rangle = \int \frac{d^4 p}{(2\pi)^4} e^{ip\...
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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 ...
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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 ...
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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 &...
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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 ...
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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, ...
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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 ...
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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 ...
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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
$$
\tag 1 \kappa \equiv \...
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Topological susceptibility of electroweak theta-term
Suppose EW theory generating functional:
$$
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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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 ...
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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 ...
3
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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 ...
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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 ...
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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 ...
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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:
...
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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 ...
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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 ...
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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, ...
3
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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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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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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,
...
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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 ...
2
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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 ...
2
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$SU(2)$ 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:
$$W=\frac{{\...
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QCD generating functional and QCD vacuum from nonperturbative to perturbative regime!
The complete generating functional in QCD (starting from the most general renormalizable, Lorentz invariant and gauge invariant Lagrangian) given by $$Z_\theta[J]=\int \mathcal{D}A \exp i\int d^4x~ {\...
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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 ...
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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 ...
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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 (...
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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 (...
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Theory with interaction and the birth of bound states during propagation
Suppose we want to calculate vacuum expectation
$$
\tag 1 D_{lm}(x - y) = \langle \Omega | \hat {T}\left( \hat {\Psi}_{l}(x)\hat {\Psi}_{m}^{\dagger}(y)\right)| \Omega\rangle = \langle \Omega| \hat {...
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Definition of a non-pertubative Quantum field theory
How do you define a non-perturbative Quantum field theory. What does it mean? I was just digging around some math about the meaning of $Z_1$, and such in terms of probabilities. It turns out these and ...
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Can all classical optical materials be described by perturbation theory?
In quantum field theory (e.g. lattice QED), perturbation theory can "break down" when interactions become too strong.
Can something like that happen in classical non-linear optics? Can there ...
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Why is it justified to focus on gauge transformations constant at spatial infinity in QCD instantons?
In the context of Yang-Mills theories and QCD instantons, much of the literature and conventional treatment hinges on the consideration of gauge transformations that remain constant at spatial ...
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Is QCD parity conserving also non-perturbatively?
Since QCD is fundamentally non-perturbative at low energies one may ask if QCD is still Parity conserving. In the path-integral formalism using the Faddeev–Popov ghosts as gauge fixing terms the ...
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Do Universal Spacetimes have Non-perturbative quantum corrections?
Universal spacetimes have the interesting property that their quantum corrections vanish to all loop orders, and can be viewed as classical solutions to speculative theories of quantum gravity like ...
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$SU(2)$ gauge supersymmetric theory and superpotential
I am currently studying supersymmetry and I came across a superpotential of the following form
$$W=\frac{\Lambda^5}{\bar{Q}Q}+m\bar{Q}Q.$$
The first term is said to appear as a result of non-...
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1
answer
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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 ...
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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 ...
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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. ...
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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 ...
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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, ...
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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 ...
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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,...