Gauge invariant incorporation of particle widths?

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Discussion Overview

The discussion revolves around the incorporation of particle widths into theoretical models while maintaining gauge invariance. Participants explore various methods and implications of these approaches, focusing on the theoretical and mathematical aspects of gauge invariance in particle physics.

Discussion Character

  • Debate/contested
  • Technical explanation
  • Mathematical reasoning

Main Points Raised

  • One participant suggests that introducing particle width via the Breit-Wigner propagator can break gauge invariance and seeks alternative methods to incorporate widths while retaining this invariance.
  • Another participant references a paper that may provide insights into the issue, indicating that there are existing approaches to consider.
  • A proposed method involves replacing m^2 in denominators with (m-iγ/2)^2, although concerns are raised about its effectiveness in preserving gauge invariance.
  • One participant expresses skepticism about the proposed method, noting that it merely adds a term quadratic in "gamma" and does not restore gauge invariance in specific cases like Compton scattering and electron-positron annihilation.
  • Another participant argues that if an approximation breaks gauge invariance, one can still perform calculations within that gauge without needing gauge invariance for approximate calculations.
  • A participant emphasizes the importance of having a gauge invariant amplitude due to suspected strong cancellations in the process they are studying and questions which gauge would be appropriate for inserting widths into propagators.

Areas of Agreement / Disagreement

Participants exhibit disagreement regarding the effectiveness of various methods to incorporate particle widths while maintaining gauge invariance. There is no consensus on a definitive approach or solution.

Contextual Notes

Some methods discussed may depend on specific conditions or assumptions that are not fully explored, and the implications of breaking gauge invariance in approximations are not resolved.

Who May Find This Useful

Researchers and students interested in particle physics, gauge theories, and the mathematical formulations of particle widths may find this discussion relevant.

EL
Science Advisor
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Introducing particle width via the Breit-Wigner propagator can break gauge invariance.
Anyone know of some "nice" way to incorporate widths while still retaining gauge invariance?
 
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You could try replacing m^2 in denominators by (m-i\gamma/2)^2.
If that breaks GI, just stay in that particular gauge.
 
I'm not really able to see how that method gives hope to retain gauge invariance if the ordinary Breit-Wigner fails? I mean, all it does just to add one more term, quadratic in "gamma", in the denominators?

(And for two simple cases I've checked, Compton scattering and electron-positron annihilation, it doesn't help to restore GI.)
 
If an approximation breaks GI. You can do everything in that gauge.
You don't need GI to complete an approximate calclation.
 
I would like to have a gauge invariant amplitude since I suspect strong cancelations are important in the certain process I'm interested in.

If I do as you suggest and just stick to a certain gauge, which one is the "correct" to be in when I insert the width in the propagators?
 

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