A question about the minimal vertex possible

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Discussion Overview

The discussion centers around the concept of bilinear vertices in quantum field theory, specifically addressing the implications of having a fundamental vertex with one particle entering and another exiting. Participants explore the theoretical constraints and conservation laws that may be violated by such vertices, as referenced in David Griffiths' "Introduction to Elementary Particles."

Discussion Character

  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • Ariel questions the conservation laws that would be violated by a bilinear vertex involving two different fields, as suggested by Griffiths.
  • Polyrhythmic explains that such a vertex is deemed unphysical because it arises from a misidentification of fields, which can be removed by a gauge transformation.
  • Polyrhythmic argues that if a field can be removed by a gauge transformation, it indicates that the field is not physically relevant.
  • Polyrhythmic further asserts that if one field can change into another through interaction, it implies that the fields are not independent of each other.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the implications of gauge transformations and the independence of fields. While some points are clarified, the discussion remains open-ended regarding the foundational principles involved.

Contextual Notes

The discussion touches on the nuances of gauge transformations and their implications for the physical relevance of fields, but does not resolve the underlying assumptions or definitions that govern these concepts.

ariel97
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hi

in "Introduction to Elementary Particles" ed. 2 / David Griffiths
the writer states that a bilinear vertex in two different fields is always impossible (my words).
or in other words: theoretically we can't have a fundamental vertex with one particle coming in and one going out.

and I feel like an idiot asking, but I have to ask since to the writer it seems obvious that I should know why, and unfortunately I don't. Which conservation laws does it violate?

I'll appreciate any answer.
Thank you
Ariel
 
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Are you referring to the statement on pages 366/367? He explains that this vertex arises through a wrong identification of the fields, and that one of the involved fields can be removed by a gauge transformation (which makes it quite unphysical). Furthermore, such a vertex would mean that the fields couldn't exist independently of each other.
 
Polyrhthmic, thanks for your answer. Yes I guess I am (although in my edition it's on a different page). That's what I'm referring to. Though I'd appreciate an explanation:
1. how do you conclude that a field which can be removed by a gauge transformation is unphysical?
2. why is it that such a vertex would mean that the fields interacting in it couldn't exist independently?

thank you.
 
ariel97 said:
Polyrhthmic, thanks for your answer. Yes I guess I am (although in my edition it's on a different page). That's what I'm referring to. Though I'd appreciate an explanation:
1. how do you conclude that a field which can be removed by a gauge transformation is unphysical?
2. why is it that such a vertex would mean that the fields interacting in it couldn't exist independently?

thank you.

1. Gauge transformations relate physically equivalent systems. If the system with the field is equivalent to a system with an absent field, the field isn't physically relevant.

2. Because that would mean that one field changes into another through some sort of interaction, it is therefore not independent.
 
thank you Polyrhythmic, you really helped me. (:
 
You're welcome!
 

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