advanced_notions:quantum_field_theory:perturbation_theory
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advanced_notions:quantum_field_theory:perturbation_theory [2017/12/17 16:22] jakobadmin [Why is it interesting?] |
advanced_notions:quantum_field_theory:perturbation_theory [2018/10/11 16:16] (current) jakobadmin [Abstract] |
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| ====== Perturbation Theory ====== | ====== Perturbation Theory ====== | ||
| - | <tabbox Why is it interesting?> | + | //see also [[advanced_tools:feynman_diagrams|]] // |
| + | <tabbox Inutuitive> | ||
| + | <blockquote> | ||
| + | Perturbation theory is a large collection of iterative methods for obtaining approximate solutions to problems involving a small parameter $\epsilon$. These methods are so powerful that sometimes it is actually advisable to introduce a parameter $\epsilon$ temporarily into a difficult problem having no small parameter, and then finally to set $\epsilon =1$ to recover the original problem. This apparently artificial conversion to a perturbation problem may be the only way to make progress. | ||
| - | [{{ :quantum_theory:quantum_field_theory:perutrbation_theory.png?nolink |source: http://faculty.washington.edu/acherman/PCM_Resurgence.pdf}}] | + | The thematic approach of perturbation theory is to decompose a tough problem into an infinite number of relatively easy ones. Hence, perturbation theory is most useful when the first few steps reveal the important features of the solution and the remaining ones give small corrections. |
| - | ---- | + | <cite>[[https://www.springer.com/de/book/9780387989310|Advanced mathematical methods for scientists and engineers]] by Bender and Orszag</cite> |
| - | + | </blockquote> | |
| - | **Important Related Concepts:** | + | |
| - | + | ||
| - | * [[advanced_tools:feynman_diagrams|]] | + | |
| - | <tabbox Layman> | + | |
| - | + | ||
| - | <note tip> | + | |
| - | Explanations in this section should contain no formulas, but instead colloquial things like you would hear them during a coffee break or at a cocktail party. | + | |
| - | </note> | + | |
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| - | <tabbox Student> | + | <tabbox Concrete> |
| <note tip> | <note tip> | ||
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| </note> | </note> | ||
| - | <tabbox Researcher> | + | <tabbox Abstract> |
| - | <note tip> | + | * [[https://arxiv.org/abs/1704.05067|Amplitudes for Astrophysicists I: Known Knowns]] by Daniel J. Burger et. al. |
| - | The motto in this section is: //the higher the level of abstraction, the better//. | + | <tabbox Why is it interesting?> |
| - | </note> | + | |
| - | --> Common Question 1# | + | [{{ :quantum_theory:quantum_field_theory:perutrbation_theory.png?nolink |source: http://faculty.washington.edu/acherman/PCM_Resurgence.pdf}}] |
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| - | <-- | ||
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| - | --> Common Question 2# | ||
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| - | <-- | ||
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| - | <tabbox Examples> | ||
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| - | --> Example1# | ||
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| - | <-- | ||
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| - | --> Example2:# | ||
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| - | |||
| - | <-- | ||
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| - | <tabbox History> | ||
| </tabbox> | </tabbox> | ||
advanced_notions/quantum_field_theory/perturbation_theory.1513524166.txt.gz · Last modified: 2017/12/17 15:22 (external edit)
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