# Lagrangian of fields from Feynman diagrams

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1. Aug 31, 2015

### Garrulo

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

2. Aug 31, 2015

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

3. Aug 31, 2015

### Demystifier

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.

4. Aug 31, 2015

### 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?

5. Aug 31, 2015

### Demystifier

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

6. Aug 31, 2015

### Demystifier

Sorry, I still don't understand the question.

7. Aug 31, 2015

### 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?

8. Aug 31, 2015

### 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.

9. Aug 31, 2015

### Garrulo

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

10. Aug 31, 2015

### 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.

11. Aug 31, 2015

Staff Emeritus
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?

12. Aug 31, 2015

### 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.

13. Aug 31, 2015

### 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

14. Aug 31, 2015

### 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.)

15. Sep 1, 2015

### 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??

16. Sep 1, 2015

### Demystifier

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.

17. Sep 1, 2015

### Garrulo

Do you know any web site 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

18. Sep 1, 2015

### Demystifier

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

19. Sep 1, 2015

### Avodyne

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

20. Sep 1, 2015

### Garrulo

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

21. Sep 1, 2015

### 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??