Introductory texts about QFT, stressing the connections to non-relativistic QM

[kith]

Hello!

I'm quite familiar with non-realtivistic QM and particle phenomenology. What I do really miss is a text, which builds on the postulates of quantum mechanics and stresses the similarities and differences between "single particle" nonrelativistic QM and QFT. I want to read about measurements, localized states, Hamiltonians, the absence of position operators, potential wells, etc. QFT is regarded the more fundamental theory, so why don't so many authors put any effort in getting back "single particle" QM out of it or at least draw more connections?

Instead, most texts jump directly to applied relativistic QFT, which goes like "Hey, you know classical field theory? Let's just take such wave equations, get plane wave solutions, quantisize them, calculate transition matrix elements and draw funny pictures. Oh, and there are symmetries, too."

Any recommendations?

 

[meopemuk]

You can check the other thread https://www.physicsforums.com/showthread.php?t=474666

Eugene.

 

[A. Neumaier]

I'm quite familiar with non-realtivistic QM and particle phenomenology. What I do really miss is a text, which builds on the postulates of quantum mechanics and stresses the similarities and differences between "single particle" nonrelativistic QM and QFT.

Weinberg's book on QFT does the best job in this respect.

I want to read about measurements, localized states, Hamiltonians, the absence of position operators, potential wells, etc.

You can read there about Hamiltonians but not the other stuff.

Try my theoretical physics FAQ at http://arnold-neumaier.at/physfaq/physics-faq.html for the remaining questions, and then perhaps ask about things not described there.

 

[Demystifier]

Kith, there is an old but very good QFT textbook that extensively discusses some of the issues you want:
S. Schweber, Introduction to Relativistic Quantum Field Theory
Despite the title, it discusses the nonrelativistic case in much detail.

 

[kith]

You can check the other thread https://www.physicsforums.com/showthread.php?t=474666

Sorry, but reading about your personal theory is useless for me, since I don't know mainstream QFT yet. This is what I'm asking about here.

 

[kith]

@Neumaier & Demystifier:
Thanks! I will check out Weinberg and Schweber.

Further suggestions are welcome

 

[bg032]

Sorry, but reading about your personal theory is useless for me, since I don't know mainstream QFT yet. This is what I'm asking about here.

Mainstream QFT is exactly the kind of QFT which makes you so unsatisfied. I had a problem very similar to yours, and I found the book of meopemuk very useful.

 

[qsa]

Hello!

I'm quite familiar with non-realtivistic QM and particle phenomenology. What I do really miss is a text, which builds on the postulates of quantum mechanics and stresses the similarities and differences between "single particle" nonrelativistic QM and QFT. I want to read about measurements, localized states, Hamiltonians, the absence of position operators, potential wells, etc. QFT is regarded the more fundamental theory, so why don't so many authors put any effort in getting back "single particle" QM out of it or at least draw more connections?

Instead, most texts jump directly to applied relativistic QFT, which goes like "Hey, you know classical field theory? Let's just take such wave equations, get plane wave solutions, quantisize them, calculate transition matrix elements and draw funny pictures. Oh, and there are symmetries, too."

Any recommendations?

the kind of problems you mention is not restricted to physics but permeates all human activities that are at a high level, and sometimes not so high. That is why PHDs are held in high regard , because they sift through incredible amount of info from different view points and try to reach something that makes "sense".

When I was introduced to accounting, Oracle software people kept educating me by telling me that accounting is "cut &dry"(some strict rules) but after some years I discovered that acounting is the dirtiest kitchen you ever been to, you can make your own rules if you are smart. That is how you got the financial meltdown. And don't let me start on describing the physics kitchen.

The irony is that as more people feel they can explain better you get more view points which adds to the confusion (add fuel to the fire). but the similarities of the different view points does give some comfort. Also schools are basically designed to get people to hold some job later and not really understand. but when you study on your own you will miss the teachers input but you do gain the hard earned knowledge.

this one is the best I could find.

http://www.quantumfieldtheory.info/

here is a quote from the site

Probability Density in Relativistic QM and QFT Updated version is now part of Chap. 3 above. The differences between probability density in non-relativistic quantum mechanics and relativistic quantum theories. A confusing topic for students not explained in any text known to the author.

 

[kith]

the kind of problems you mention is not restricted to physics but permeates all human activities that are at a high level, and sometimes not so high. That is why PHDs are held in high regard , because they sift through incredible amount of info from different view points and try to reach something that makes "sense".

What you say certainly has its truth. Still, my impression is that in the case of QFT, the connections to the "parent" theory are more rarely pointed out than in other branches of physics. E.g. SR <-> GR, Classical Mechanics <-> QM, etc.

Anyway, thanks for your contribution! This site looks interesting, indeed.