# Tag Info

## Hot answers tagged non-perturbative

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Perturbative theory is understood as an application of the Taylor expansion around a linearity $g=0$ (unperturbed theory) in an underlying theory: $$f(g)=\sum_{n}A_n g^n$$ The unperturbed theory could be, for example, an Hydrogen Atom for the underlying QED. Then, the QED perturbative theory is a prescription of how inserting $g\neq0$ corrections of the ...

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There are many phenomenon in quantum field theory that falls outside the understanding of perturbative analysis. To understand the nonperturbative physics is to understand the full dynamics of the theory whereas perturbation theory is not reliable. The basic examples are 1) dynamical symmetry breaking (supersymmetry or chiral symmetry) which is usually ...

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1) As you know, $$\tag 1 \theta\epsilon^{\mu \nu \alpha \beta}F_{\mu \nu}F_{\alpha \beta} = \theta\partial_{\mu}K^{\mu},$$ where $K_{\mu}$ is the so-called Chern-Simons class. The Feynman diagrams method tells us that the term $(1)$ defines the diagram which corresponds to the two-photon (or two-three-four non-abelian bosons) vertex $V_{A}$ (where the ...

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1) $\exp(-1/g)$ is not necessarily related to bound states. In the standard QM double well problem it is the splitting, not the binding energy, that is $O(\exp(-1/g))$. In conformal field theories instantons can give $\exp(-1/g)$ effects even though there are no bound states at all. 2) Instantons are one source of $\exp(-1/g)$ effects, but there are others. ...

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Rather tautologically, a non-perturbative effect is one that is invisible to perturbation theory. An effect is invisible to perturbation theory exactly if it is in a non-analytic part of the partition function with respect to the coupling constant $g$. Observe that perturbation theory is essentially the Taylor expansion of the partition function $Z$ (or ...

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Instantons are characterized by the winding number and a set of collective parameters (e.g. location of the centers of the instantons, their sizes and the inequivalent orientations in the global group space / space-time). Quantum fluctuations of a unit winding number instanton can either leave the collective parameters unchanged (non-zero modes), or change ...

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Here is one possible way to evaluate this expression using FeynCalc: << FeynCalc` SUNF[a1, a2, a3] SUNF[a4, a2, a7] SUNF[a7, a8, a1] SUNF[a5, a6, a3] * SUNF[a9, a4, a5] SUNF[a8, a9, a6] // SUNSimplify[#, Explicit -> True, SUNNToCACF -> False] & // Simplify and the answer is: 1/4 SUNN^3 (-1 + SUNN^2) i.e. what the OP got from doing the ...

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The baryon non-conservation in the quantum theory is caused by the chiral anomaly, which leads to the baryon current $j_B^\mu = \sum_i \bar q_i \gamma^\mu q_i$ being not conserved as $$\partial_\mu j_B^\mu \propto F\wedge F$$ where $F$ is the field strength tensor of the electroweak field. Now, $\int \partial_\mu j_B^\mu \propto \int F\wedge F$ is a ...

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The bare coupling vanishes in the continuum limit, because the renormalized quantities are associated with measurements over very large scales (compared to the lattice spacing). One way to think about this is that since QCD is confining, the coupling at the scale of the lattice spacing must vanish if the coupling at the continuum scale is to remain finite. ...

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