Questions tagged [non-perturbative]
Use this for questions which discuss models of quantum theories which do not make use of peturbation theory.
154
questions
0
votes
0
answers
14
views
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, ...
1
vote
0
answers
34
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 ...
1
vote
0
answers
34
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 ...
1
vote
2
answers
158
views
1PI effective action and Action generated through Hubbard-Stratonovich transformation
In standard lectures on advanced QFT one learnt that performing Legendre transformation leads to effective actions generating one-particle-irreducible (1PI) diagrams, which is encoded by Schwinger-...
2
votes
0
answers
74
views
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,
...
0
votes
1
answer
140
views
Why does non-perturbative QCD need to be regularized and renormalized?
The $n$-point correlation functions of QCD, which define the theory, are computed by performing functional derivatives on $Z_{QCD}[J]$, the generating functional of QCD,
$$\frac{\delta^nZ_{QCD}[J]}{\...
0
votes
1
answer
227
views
Does the current form of non-perturbative QFT make all the same predictions as perturbative QFT, or is it incomplete?
For context, I watched PBS Spacetime's video on virtual particles (link goes to relevant timestamp) where they say that virtual particles aren't mathematically necessary, because the lattice version ...
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 ...
2
votes
0
answers
75
views
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 ...
6
votes
0
answers
89
views
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 ...
2
votes
1
answer
53
views
Perturbative non-renormalizability and viability?
Does perturbative non-renormalizability indicate the unviability of the theory if we were to define it non-perturbatively (for example through a lattice discretization of the continuum QFT or other ...
4
votes
2
answers
317
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 ...
3
votes
0
answers
141
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 ...
3
votes
0
answers
68
views
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 ...
4
votes
1
answer
170
views
How does AdS/CFT help us understand non-perturbative aspects of QCD?
I've heard AdS/CFT has found applications in many areas of physics where nonperturbative aspects leave us crippled in making any simple calculations.
Among these applications, I also have heard that ...
-1
votes
1
answer
71
views
Why do we assume the coupling is small in Dyson series?
I’ve seen people say that if the coupling constant is large, we can’t trust Feynman Diagrams (like in the case of QCD). The logic is that high couplings describe bound states, whereas Feynman Diagrams ...
2
votes
1
answer
89
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 ...
1
vote
2
answers
203
views
Is the Rayleigh–Schrödinger perturbation theory ever useful for a many-body system?
The Rayleigh-Schrodinger perturbation theory is introduced in every textbook on quantum mechanics. It seems that it can yield accurate results for many single-particle systems. Actually, in most ...
2
votes
1
answer
170
views
Non-perturbative approach to high-energy physics
I know that main numerical approach to modeling high-energy physics events are Monte-Carlo event generators. But they are using perturbative description of collision and decay processes of particles.
...
0
votes
0
answers
63
views
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,...
6
votes
0
answers
129
views
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 &...
0
votes
0
answers
63
views
Evolution operator as a Laurent series of coupling constant
Let the Hamiltonian be $H_{0}+gV$, where $g$ is the coupling constant. In the interaction picture, the equation for the evolution operator is $i\frac{dU}{dt}=gV_{I}U$. What I am going to do is assume $...
0
votes
1
answer
115
views
Should the $S$-matrix always analytic in coupling constant?
If we use Dyson series, the $S$-matrix is always an analytic function of the coupling constant. However, if that is the case, how can non-perturbative effects arise in QFT? My question is, should the $...
1
vote
1
answer
164
views
What is the difference between a perturbative and a non-perturbative vacuum?
What is the difference between a perturbative and a non-perturbative vacuum in quantum field theory? Is there an analog of these ideas in non-relativistic quantum mechanics?
8
votes
0
answers
187
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 ...
3
votes
0
answers
221
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 ...
1
vote
0
answers
84
views
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 ...
1
vote
2
answers
269
views
Functional Renormalization Group and Dirac Fermions — Yukawa Theory
I've been practicing with FRG techniques and I wanted to obtain the usual beta functions for Yukawa theory using the Wetterich equation. However, this has been more troublesome than I expected.
If I'm ...
3
votes
0
answers
132
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. ...
0
votes
1
answer
88
views
What are some good resources to learn about perturbative and non-perturbative approaches to QCD, for example Lattice QCD, at an introductory level?
I am writing at an introductory level about the anomalous magnetic moment of the muon and part of that is the subsequent Lattice QCD that potentially verifies the results from the experiments that ...
1
vote
0
answers
58
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 ...
1
vote
1
answer
78
views
Did $\int dx^4 \partial ^\mu \phi(x) \partial_\mu \phi(x)= -\int dx^4 \phi(x) \partial^2 \phi(x)$ in the path integral formalism?
In the canonical quantization, one assumed the condition that the field $\phi(x)$ vanished at both space and time infinity.
However, in the path integral formalism, thought the field $\phi(x)$ was ...
1
vote
1
answer
122
views
Non-Perturbative Effects Of Soliton in Quantum Field Theory
I am reading Quantum Field Theory in a Nutshell by A.Zee. In Chapter 5 Section 6, Under the subtitle A nonperturbative phenomenon, He commented
"That the mass of the kink comes out inversely ...
9
votes
1
answer
595
views
Old-fashioned perturbation theory and contribution from resonances
In his QFT vol. 1 (paragraph 3.5), Weinberg discusses the so-called old-fashioned perturbation theory (OFPT), i.e. the one based on the perturbative expansion of the Hamiltonian. As a result, in this ...
0
votes
0
answers
53
views
Physical interpretation of hadron distribution amplitudes
A parton fragmentation function can be interpreted as the probability that a final state hadron originated from that particular hadron.
A parton distribution function can be interpreted as the ...
4
votes
0
answers
75
views
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, ...
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{{\...
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-...
5
votes
1
answer
496
views
When does QFT perturbation theory stop being valid?
When introduced to the concept of perturbation theory in Quantum Mechanics we split the hamiltonian $H= H_0 + \delta H$ where $\delta H$ is small in some manner, ie if say $\epsilon$ is the relevant ...
0
votes
1
answer
379
views
Does quantum field theory exist non-perturbatively or is perturbation inherent to its Nature?
In quantum field theory, calculations generally are made by using a perturbation approximation with the aid of Feynman diagrams. The theory is not well suited for bound states as Feynman diagrams ...
4
votes
0
answers
153
views
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 ...
3
votes
0
answers
208
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:
...
7
votes
1
answer
2k
views
Hydrogen atom in quantum field theory
In principle, how would we demonstrate the existence of the hydrogen atom in quantum field theory and the standard model?
Has it been done in practice?
Some naive ideas:
Demonstrate that the familiar ...
2
votes
1
answer
202
views
What's the difference between operator product expansion and perturbation?
Operator product expansion and perturbation theory both looked somewhat similar to Taylor/Laurent series expansion.
Quote: Conformal Field Theory, Philippe Di Francesco, Pierre Mathieu, David Senechal,...
2
votes
1
answer
219
views
Canonical quantization
I am looking for a generic treatment or a concrete example where canonical quantization is performed without using free fields. For a scalar field
$$\phi(x,t) \sim \sum_k \phi_k{(t)} \, u_k(x) + \...
4
votes
3
answers
634
views
How is $\Lambda_{\textrm{QCD}}$ relevant in the non-perturbative regime?
The famous $\Lambda_{\textrm{QCD}}$ parameter enters through the one-loop running of the QCD coupling, through a relation similar to the following:
$$\alpha_S(Q^2)=\frac{\alpha_S(Q^2_0)}{1+b\ln(Q^2/Q^...
3
votes
0
answers
135
views
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 ...
3
votes
0
answers
116
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 ...
5
votes
2
answers
171
views
Besides instantons and large-$N$ what are some other general non-perturbative methods for quantum field theory?
Besides large-$N$, instantons, lattice QFT, what are some other non-perturbative methods that help us better understand QFTs like the large distance dynamics of Yang Mills and QCD?
2
votes
0
answers
150
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~ {\...