# A question about the minimal vertex possible

• ariel97
In summary, the writer in "Introduction to Elementary Particles" explains that a bilinear vertex in two different fields is impossible and would violate conservation laws. This is due to the wrong identification of fields and the ability to remove one of the fields through a gauge transformation. Such a vertex would also imply that the fields cannot exist independently.
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?

Thank you
Ariel

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!

## 1. What is the minimal vertex possible?

The minimal vertex possible refers to the smallest or lowest number of vertexes that can be present in a given graph or mathematical structure.

## 2. How is the minimal vertex possible calculated?

The calculation of the minimal vertex possible depends on the type of graph or mathematical structure being considered. In general, it involves identifying the smallest number of vertexes that can still maintain the essential properties of the given structure.

## 3. Can the minimal vertex possible change?

Yes, the minimal vertex possible can change depending on the conditions or constraints placed on the graph or mathematical structure. For example, adding or removing edges can affect the minimal vertex possible.

## 4. What is the significance of the minimal vertex possible?

The minimal vertex possible is important because it provides insight into the complexity and structure of a graph or mathematical problem. It can also help in finding efficient solutions and algorithms for solving problems related to the given structure.

## 5. Are there any real-world applications of the concept of minimal vertex possible?

Yes, the concept of minimal vertex possible has various real-world applications, such as in computer networks, social networks, and transportation systems. It can also be applied in optimization problems, scheduling, and resource allocation.

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