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The perturbative treatment of the Stark effect has some problems.
This is because perturbative calculations are done in the interaction picture.
The bands of interest can be then described by various effective models, usually based on some perturbative approach.
Flush-mounted probes, on the other hand, being part of the wall, are less perturbative.
However, it was found to be a regularization suitable also for perturbative calculations.
This perturbative framework can be applied to most of the long-baseline experiments.
There is absolutely no guarantee that perturbative methods result in a convergent solution.
In two dimensions, the perturbative expansion parameter is 2/3.
This fact makes quantum electrodynamics inconsistent beyond the perturbative expansions.
The perturbative treatment becomes exact in the double scaling limit .
Higher order anharmonicity terms can be accounted by using perturbative methods.
These two main broad types can be further categorised according to whether they are based on constructive or perturbative search.
This section develops, in simplified terms, the general theory for the perturbative solution to a differential equation to the first order.
This problem is notoriously difficult to tackle theoretically, since perturbative techniques break down at low-energy.
However, this does not imply that we can do without these "unphysical" fields in the intermediate states of a perturbative calculation!
The Virial equation derives from a perturbative treatment of statistical mechanics.
Each perturbative description of string theory depends on a string coupling constant.
The number of these functions is relative to the degree of contraction of the resulting perturbative space.
In both cases, the perturbative calculation of the S-matrix leads to Feynman diagrams.
The coefficients are expected to be small because of the Planck-scale suppression, so perturbative methods are appropriate.
Perturbative aspects of QCD have been tested to a few percent.
Because of this instantons cannot be studied by using Feynman diagrams, which only include perturbative effects.
Ultraviolet divergences in perturbative quantum field theory are dealt with in renormalization.
Perturbative pions in effective field theory for nucleon interactions.
When calculating the fluctuations with a perturbative approach, the zero order approximation is Fick's law.