"WHAT IS A QUANTUM FIELD THEORY?" A First Introduction for Mathematicians

[bhobba]

The book is fascinating. If your education includes a typical math degree curriculum, with Lebesgue integration, functional analysis, etc, it teaches QFT with only a passing acquaintance of ordinary QM you would get at HS. However, I would read Lenny Susskind's book on QM first.



Purchased a copy straight away, but it will not arrive until the end of December; however, Scribd has a PDF I am now studying. The first part introduces distribution theory (and other related concepts), which I already know, but it is not presented as rigorously as in the textbook from which I learned it. As an aside, being for mathematicians, I don't know why they don't do it as a mathematician would.

Thanks
Bill

 

[dextercioby]

Let me guess, the standard math style «definition, theorem, corrolary» is not there.

 

[bhobba]

Let me guess, the standard math style «definition, theorem, corrolary» is not there.

That's not what I meant.

I meant a treatment, while still somewhat informal, is still rigorous, as found in:
https://www.amazon.com.au/Theory-Distributions-Nontechnical-Introduction-ebook/dp/B01DM26TPW

He defines Schwartz distributions well, but then presents a 'cutoff' type argument to perform Fourier transforms.

The easiest way is <F(f(x))|u(x)> = <f (x)|F(u(x)) where u(x) is a Schwartz test function.

Easy-peasy. It can also be shown that any good function has a Fourier transform.

He mentions it in a note so those interested can look into it. Maybe he is preparing for cutoff-type arguments in renormalisation - I don't know.

Thanks
Bill

 

[mad mathematician]

Well, I've got two books that treat QFT for the math-geared ahead (I double majored in maths and physics), they kind of old. There's Ticcati's red book and Folland's.

Didnt finish reading them though...

 

[dextercioby]

Well, I've got two books that treat QFT for the math-geared ahead (I double majored in maths and physics), they kind of old. There's Ticcati's red book and Folland's.

Didnt finish reading them though...

Speaking of Folland's books, they are notorious for typos. Here's the errata for his 1st edition of the QFT book.

 

[mad mathematician]

Speaking of Folland's books, they are notorious for typos. Here's the errata for his 1st edition of the QFT book.

Thanks.

 

[MidgetDwarf]

Speaking of Folland's books, they are notorious for typos. Here's the errata for his 1st edition of the QFT book.

Is it the same for his 2 Fourier books, and his Real Analysis book?

 

[dextercioby]

Is it the same for his 2 Fourier books, and his Real Analysis book?

Of course. All have erratas.