Fine structure constant and perturbation theory

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SUMMARY

This discussion centers on the relationship between the fine structure constant and perturbation theory in quantum electrodynamics. It confirms that while the same Feynman diagrams are used regardless of the value of the fine structure constant (α), their contributions vary significantly with different values of α. A smaller α results in higher-order diagrams having less influence, whereas a larger α leads to substantial contributions from many diagrams. This principle is also illustrated by the strong force, where a large coupling constant complicates perturbative calculations.

PREREQUISITES
  • Understanding of quantum electrodynamics (QED)
  • Familiarity with Feynman diagrams
  • Knowledge of perturbation theory
  • Concept of vacuum polarization
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  • Research the implications of varying the fine structure constant on quantum electrodynamics
  • Study the role of vacuum polarization in particle physics
  • Learn about perturbation theory in the context of quantum field theory
  • Examine the differences between perturbative and non-perturbative approaches in quantum mechanics
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Physicists, particularly those specializing in quantum mechanics and quantum field theory, as well as students and researchers interested in the implications of fundamental constants in particle interactions.

asimov42
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Hi all,

I have a question about perturbation theory and the fine structure constant. Consider an electron moving through the vacuum - this wil induce vacuum polarization, and (if I understand correctly) perturbation theory can be used to analyze the situation. My question is essentially: if the fine structure constant took on a different value (as some theories predict is can), would the interaction between the electron field and the electromagnetic field be different? That is, would you draw a different sequence of Feynman diagrams for the different cases (alpha_1 vs. alpha_2) - does changing the strength of the electromagnetic interaction change the perturbative (or non-perturbative) result?

Thanks!
 
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You would draw the same sets of diagrams, but their relative strength (at different orders of alpha) would vary. With a smaller alpha, higher orders would have less influence, and with a large alpha, a lot of different diagrams would contribute significantly.

You can see this at the strong force: It has a large coupling constant, and perturbative calculations are much more difficult there.
 

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