Books for the Mathematics of Feynman Diagrams

[Sunnyocean]

Summary:: What is (are) the best book(s) to understand the mathematics of Feynman diagram?

Hello,

Can anyone recommend some books for the mathematics of Feynman diagram? (I don't mind if they also include the physics; in fact it may be better).

Ideally I would need books that are very detailed (they don't skip steps in proofs to theorems, solutions to exercises etc.) but, at the same time, they take you from the basic level to a very advanced level.

 

[Vanadium 50]

You are unlikely to find one. There are many books on field theory, but likely zero that cover just Feynman diagrams.

 

[haushofer]

Aren't you just looking for QFT-texts? Or are these not rigorous enough?

 

[Milsomonk]

I'm unaware of any books specifically dedicated to Feynman diagrams, but an entry level QFT text should have a lot of what you are looking for. I found Peskin Schroeder (An Introduction to Quantum Field Theory) very useful when studying for my masters, and still lean on it on the occasion I need to revisit such things as Feynman diagrams. The first part sets out the calculational tools required for QFT, which in this context means the formalism of Feynman diagrams.

Failing this some Universities may publish their lecture notes online for courses on QFT/QED which may be helpful in introducing and justifying the existence of Feynman diagrams.

 

[PeroK]

Summary:: What is (are) the best book(s) to understand the mathematics of Feynman diagram?

Hello,

Can anyone recommend some books for the mathematics of Feynman diagram? (I don't mind if they also include the physics; in fact it may be better).

Ideally I would need books that are very detailed (they don't skip steps in proofs to theorems, solutions to exercises etc.) but, at the same time, they take you from the basic level to a very advanced level.

You're not going to like this. The Feynman diagrams represent the terms in an infinite (Dyson) series of integrals. But, the infinite series diverges(!) If you are looking for a rigorous proof of the mathematics of Feynman diagrams you'll be disappointed. The Feynman diagrams use the concept of an optimal asymptotic approximation.

As others have said, this would normally be covered in a chapter in a QFT book.

There are other techniques for summing a divergent series, such as Borel-Pade summation. This branch of applied maths includes much that can be proved rigorously (a lot was done by Stieltjes) but also results involving continued fractions and the like that appear to work but cannot be proved.

 

[haushofer]

You're not going to like this. The Feynman diagrams represent the terms in an infinite (Dyson) series of integrals. But, the infinite series diverges(!) If you are looking for a rigorous proof of the mathematics of Feynman diagrams you'll be disappointed. The Feynman diagrams use the concept of an optimal asymptotic approximation.

As others have said, this would normally be covered in a chapter in a QFT book.

There are other techniques for summing a divergent series, such as Borel-Pade summation. This branch of applied maths includes much that can be proved rigorously (a lot was done by Steiltjes) but also results involving continued fractions and the like that appear to work but cannot be proved.

Being Dutch I have to correct you: it's "Stieltjes"

To also post something useful: I really liked the follwing notes:

https://arxiv.org/abs/1201.2714

 

[PeroK]

Being Dutch I have to correct you: it's "Stieltjes"

To also post something useful: I really liked the follwing notes:

https://arxiv.org/abs/1201.2714

Thanks. I was distracted by trying to get the l-t-j in the right order!

 

[TeethWhitener]

I have this one:
https://www.amazon.com/dp/0486670473/?tag=pfamazon01-20
It’s cheap and engagingly written.

Edit: above link is broken. Here’s the google books preview:
https://books.google.com/books/about/A_Guide_to_Feynman_Diagrams_in_the_Many.html?id=pe-v8zfxE68C

 

[jim mcnamara]

@TeethWhitener - seems to be a broken link, not connecting as an Amazon user.

 

[TeethWhitener]

@TeethWhitener - seems to be a broken link, not connecting as an Amazon user.

Fixed, thanks.

 

[AndreasC]

You're not going to like this. The Feynman diagrams represent the terms in an infinite (Dyson) series of integrals. But, the infinite series diverges(!) If you are looking for a rigorous proof of the mathematics of Feynman diagrams you'll be disappointed. The Feynman diagrams use the concept of an optimal asymptotic approximation.

As others have said, this would normally be covered in a chapter in a QFT book.

There are other techniques for summing a divergent series, such as Borel-Pade summation. This branch of applied maths includes much that can be proved rigorously (a lot was done by Stieltjes) but also results involving continued fractions and the like that appear to work but cannot be proved.

I'm interested, what branch of applied mathematics is that and what would I read to learn more?

 

[PeroK]

I'm interested, what branch of applied mathematics is that and what would I read to learn more?

I learned it from Carl Bender's lectures on YouTube:

 

[Demystifier]

There are several books specialized in math and physics of Feynman diagrams:

S.M. Bilenky, Introduction to Feynman Diagrams

A. Grozin, Lectures on QED and QCD: Practical Calculation and Renormalization of One- and Multi-Loop Feynman Diagrams

V. A. Smirnov (3 books):
- Analytic Tools for Feynman Integrals
- Evaluating Feynman Integrals
- Feynman Integral Calculus

G. 't Hooft and M. Veltman, Diagrammar

M. Veltman, Diagrammatica: The Path to Feynman Diagrams

I.T. Todorov, Analytic Properties of Feynman Diagrams

 

[MathematicalPhysicist]

There's also the book called Knots and Feynman Diagrams by Kreimer, I have this book alongsides Veltman's Diagrammatica.
Though as of yet I haven't read them.