Fine structure constant and perturbation theory

In summary, the conversation discussed the use of perturbation theory to analyze the interaction between an electron moving through vacuum and the electromagnetic field. The question was whether changing the fine structure constant would result in a different sequence of Feynman diagrams and ultimately, a different perturbative result. It was noted that while the same diagrams would be drawn, their relative strength would vary depending on the value of alpha, with a smaller alpha resulting in less influence from higher orders. The example of the strong force, which has a larger coupling constant and more difficult perturbative calculations, was also mentioned.
  • #1
asimov42
377
4
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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  • #2
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.
 

FAQ: Fine structure constant and perturbation theory

1. What is the fine structure constant and why is it important in physics?

The fine structure constant (α) is a dimensionless number that characterizes the strength of the electromagnetic interaction between elementary particles. It is important in physics because it is a fundamental constant that appears in many important equations and theories, such as quantum electrodynamics and the theory of relativity.

2. How is the fine structure constant calculated?

The fine structure constant is calculated by dividing the square of the elementary charge (e) by Planck's constant (h) multiplied by the speed of light in a vacuum (c). In mathematical terms, α = e^2 / (hc).

3. What is perturbation theory and how does it relate to the fine structure constant?

Perturbation theory is a mathematical technique used to approximate solutions to complex problems in physics. It is often used in quantum mechanics to calculate the effects of small changes or perturbations on a system. The fine structure constant appears in perturbation theory as a coupling constant, which determines the strength of the interaction between particles.

4. What is the significance of the fine structure constant being approximately equal to 1/137?

The fact that the fine structure constant is approximately equal to 1/137 is considered to be a fundamental mystery in physics. This number is a dimensionless ratio of the strengths of the electromagnetic and gravitational forces, and its small value suggests that there may be underlying symmetry or unity in the laws of physics.

5. How has our understanding of the fine structure constant evolved over time?

Our understanding of the fine structure constant has evolved significantly over time. Initially, it was thought to be a precisely defined constant, but with advances in technology and theoretical developments, scientists have discovered that it may actually vary slightly depending on the energy scale or interaction being studied. This has led to ongoing research and debate about the true nature of the fine structure constant.

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