# Book on Functional Calculus

• Calculus

## Main Question or Discussion Point

Hi, I'm looking for a book that explains more deeply (and a little bit more formal) the functional calculus than the typical introductions that I find in QFT books (like Peskin or Hatfield). Is there any good book for physicists to learn the mathematics behind functional calculus?

Thanks

## Answers and Replies

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MathematicalPhysicist
Gold Member
How about Dewitt's Functional Integration.

I must confess that I haven't read this book yet, but looks like a good place to start.

Ok, thanks, although it's not quite what I was looking for, I'm more interested in a book that starts without assuming any functional knowledge and starts constructing what a functional is, it's derivatives, functional equations etc...

MathematicalPhysicist
Gold Member
So perhaps you need a book in Calculus of Variations?

I prefer rigorous maths (when possible), so my recommendations will be as such.

Yes, if the topic is discussed in those books. I also like mathematical rigour, although I'm not a mathematician and I usually look for a trade-off between rigour and not have to read 20 books before to understand the first statement :D.

MathematicalPhysicist
Gold Member
Yes, if the topic is discussed in those books. I also like mathematical rigour, although I'm not a mathematician and I usually look for a trade-off between rigour and not have to read 20 books before to understand the first statement :D.
Well if the topic is so advanced then perhaps those 20 books are in order...

Anyway, a good place to start is An Introduction to Variational Calculus by Bernard Darcogona (google will correct my spelling). I read through chapters 1-4 didn't finish it though.

Mind you, that you need to know before that Hilbert spaces and intro to Functional Analysis.

You know all those spaces of $L^p$ etc.

vanhees71
Science Advisor
Gold Member
2019 Award
The classic still is Hilbert and Courant vol. I (not the modenized single-volume rewriting of it, which destroys the charm of the original at least somewhat).

MathematicalPhysicist
Gold Member
The classic still is Hilbert and Courant vol. I (not the modenized single-volume rewriting of it, which destroys the charm of the original at least somewhat).
yes, also that book I never finished reading.