A question about the minimal vertex possible

[ariel97]

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

 

[Polyrhythmic]

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.

 

[ariel97]

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.

 

[Polyrhythmic]

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.

 

[ariel97]

thank you Polyrhythmic, you really helped me. (:

 

[Polyrhythmic]

You're welcome!