Quantum "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...