Lagrangian of fields from Feynman diagrams

[Garrulo]

¿How is possible deduce the Lagrangian of the fields of a theory knowing only his Feynman Diagrams?

 

[Vanadium 50]

Why do you think it's possible? One Lagrangian gives you an infinite number of diagrams.

 

[Demystifier]

¿How is possible deduce the Lagrangian of the fields of a theory knowing only his Feynman Diagrams?

It's easy to deduce the Lagrangian from the Feynman rules. From the vertex rule you can deduce the interaction Lagrangian, and from the line rule you can deduce the propagator and hence the free Lagrangian.

 

[Garrulo]

But how can I know what operators (differentiation, product, etc...) must have every term from interaction between fields or from the free field terms?

 

[Demystifier]

But how can I know what operators (differentiation, product, etc...) must have every term from interaction between fields or from the free field terms?

I'm not sure I understand the question. Can you give me an example?

 

[Demystifier]

Sorry, I still don't understand the question.

 

[Garrulo]

L=ψ¯(iγμDμ−m)ψ This is the electrodebil lagrangian (but my question is general about the other fields)

I know the fermion field appears first in a free term conjugate multipluing gamma matrix and after (second term of the parenthesis) not free but interacting with the field B. ¿How can I know that the interaction term is a product and the free term is a differentiation. Free lagrangian can appear with differentiation and interaction terms can appear multiplying or with another operation. How can I know it?

 

[Avodyne]

Derivatives in the lagrangian lead to factors of momentum in the Feynman rule (either in the propagator for a 2-field term, or in a vertex for 3-or-more field term). Local products of fields in the lagrangian lead to conservation of momentum at a vertex.

This is treated in every QFT text. My personal recommendation is Srednicki, but this is covered in any of them.

 

[Garrulo]

Not, but I don´t want to how interpret the integral of Feynman diagram, I want to know the lagrangian of the field theory starting from Feynman Diagrams

 

[Avodyne]

That's exactly what I was outlining.

Propagators give you the terms in the lagrangian that are bilinear in the fields ("kinetic" and "mass" terms), vertices give you the terms in the lagrangian that involve the product of 3 or more fields ("interaction" terms). How you get the Feynman rules from the lagrangian is explained in any QFT text. Once you understand this, it is easy to go the other way: determine the lagrangian from the Feynman rules.

So: do you understand how to derive Feynman rules from a lagrangian? If not, learn that first.

 

[Vanadium 50]

From the vertex rule you can deduce the interaction Lagrangian

But how do you know that you have all the vertex rules? For example, in QCD you have a three-gluon and a four-gluon coupling. If you are only given the three-gluon coupling, how do you know what the four-gluon coupling is, at least without any new information?

 

[Avodyne]

My understanding of the OP's question is, given all the Feynman rules, how do you deduce the lagrangian? If you only have a subset of the rules, in general, you can only deduce a subset of the terms in the langrangian.

If you know something else, you might be able to do more. In your QCD example, we could deduce the 4-gluon vertex from the 3-gluon vertex if we also assume gauge invariance.

 

[Garrulo]

A Feynman diagram proportionate a term for lagrangian, it is the sum of all of them (infinite) which give us the complete lagrangian. I am not interested in doing all the sum, only to know the mechanism for transform a feynman diagram in a term of the lagrangian

 

[Avodyne]

I ask again: do you understand how to derive Feynman rules from a lagrangian, as done in any of the standard texts? (Weinberg, Peskin & Schroder, Srednicki, etc.)

 

[Garrulo]

No, in the career only explain some Feynman diagrams tree level. I know some of the books but I dont´use for work with Feynman diagramms. But in this books come the inverse explanation too, not only from lagrangian to diagram, the inverse problem too??

 

[Demystifier]

No, in the career only explain some Feynman diagrams tree level. I know some of the books but I dont´use for work with Feynman diagramms. But in this books come the inverse explanation too, not only from lagrangian to diagram, the inverse problem too??

In the books you will probably not find the inverse explanation discussed explicitly. But once you understand how to derive Feynman rules from the Lagrangian, you will be able to solve the inverse problem by yourself. It is very easy to go backwards once you know how to go forwards. But first you need to learn how to go forwards.

 

[Garrulo]

Do you know any website when it is explained singlely?? Uffff..my teachers in the career only tell me how convert the diagram in an integration, but no how deduce it from lagrangian. I don´t know if in other universities maybe you will receive better explanations

Thanks

 

[Demystifier]

Do you know any website when it is explained singlely?? Uffff..my teachers in the career only tell me how convert the diagram in an integration, but no how deduce it from lagrangian. I don´t know if in other universities maybe you will receive better explanations

Thanks

Try
http://www.phy.pmf.unizg.hr/~kkumer/articles/feynman_for_beginners.pdf

 

[Avodyne]

Srednicki's QFT text (in draft form) is freely available from his web site.

 

[Garrulo]

Thanks, I wish I can understand it. The phormulas in the first page they scared me yet xD

 

[Garrulo]

Srednicki's QFT is very easy to go on at starting but when insert green functions I don´t understand then nothing. I looked at Feynman Diagrams and the notation is strange. Do you know a e-book with a more simple level??