Quantum Field Theory for the Gifted Amateur: Fourier Transforms & Excitations

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Discussion Overview

The discussion revolves around concepts from quantum field theory, specifically focusing on Fourier transforms and the behavior of excitations in a linear chain of atoms. Participants explore the implications of Hamiltonians, equations of motion, and the coupling of frequencies within the context of the text "Quantum Field Theory for the Gifted Amateur." The scope includes theoretical understanding, mathematical reasoning, and clarification of specific equations.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • Some participants question how to demonstrate that excitations are uncoupled in frequency space, referencing specific equations from the text.
  • There is a discussion about the equations of motion for Hamiltonians 2.45 and 2.59, with some arguing that 2.45 is coupled while 2.59 is decoupled.
  • Participants express uncertainty about the implications of the Kronecker delta and its role in the cancellation of terms when m is not zero.
  • Some participants suggest that understanding the concept is crucial before performing mathematical calculations.
  • There are inquiries about the treatment of operators in Hamilton's equations and how they relate to the equations of motion.
  • One participant mentions the use of linear algebra resources to aid in understanding derivatives of operators.
  • There is confusion regarding the definitions and properties of hermitian matrices as they relate to momentum operators.
  • Some participants express frustration with the clarity of the text and seek further explanation or context for their questions.

Areas of Agreement / Disagreement

Participants exhibit a mix of agreement and disagreement, particularly regarding the coupling of frequencies and the interpretation of specific equations. Some participants assert that they can see the coupling or decoupling without extensive calculations, while others challenge this view. The discussion remains unresolved on several points, with multiple competing interpretations present.

Contextual Notes

Limitations include missing assumptions about the definitions of operators and the specific mathematical steps required to derive certain results. Participants also note the complexity introduced by the presence of operators in the Hamiltonians compared to the equations of motion.

Who May Find This Useful

This discussion may be useful for those studying quantum field theory, particularly in understanding the mathematical treatment of Hamiltonians, Fourier transforms, and the behavior of excitations in physical systems.

  • #31
I want to say that i suppose i am wrong because you don't agree and would very much like to understand why?
 
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  • #32
In eq's 3.17 and 3.18 p 33 QFT for the gifted amateur
Are the constants of proportionality ##\sqrt (n_i+1) and \sqrt n_i## explained somewhere in the book?
 
  • #33
anklimekruk said:
I want to say that i suppose i am wrong because you don't agree and would very much like to understand why?

If I understand what you meant, then it's the same I guess, but you should only ask if you're stuck somewhere. These problems are easy to figure out, we aren't being paid as tutors so you should only ask a question when you've tried everything first.

anklimekruk said:
In eq's 3.17 and 3.18 p 33 QFT for the gifted amateur
Are the constants of proportionality ##\sqrt (n_i+1) and \sqrt n_i## explained somewhere in the book?

Page 22, bottom.
 
  • #34
Thanks!
ddd123 said:
If I understand what you meant, then it's the same I guess, but you should only ask if you're stuck somewhere. These problems are easy to figure out, we aren't being paid as tutors so you should only ask a question when you've tried everything first.
Page 22, bottom.
thanks!
 
  • #35
I am really doing my best to understand before I ask a question!
May I ask if it is necessary to mention each time "QFT for the gifted amateur"
Thanks again for helping!
 
  • #36
anklimekruk said:
I am really doing my best to understand before I ask a question!

Then work on why you couldn't figure it out even if it was your best. You may need a change in method rather than effort. But anyway, you read less than 25 pages and you already missed the normalization of creation and annihilation operators which was clearly stated. It's not like you lost a minor detail after 250 pages of study...

As I said, your FIRST post asked legitimate questions, all the others were really trivial and they seem to be getting more and more trivial. I kept answering because your first questions were good questions, but it has to stop at some point. If your next question will have another obvious answer you'll have to hope someone else comes along, I can't walk you through a whole book, I have things to do...
 
  • #37
I am just a fascinated selfstudent.
I understand your time is precious and I fully respect it!
It's also a chalenge to understand things by myself.
These are two excellent reasons to do my very best to understand before asking a question.
Anyhow i am gratefull to you for all your answers.They have been helpful and instructive as well.
Thanks to you i reached p 33.
It's clear you expect a higher level but I hope you can trust me to improve with time.
If not it will be like failing the admission exams.What can i do? That's life...
 
  • #38
anklimekruk said:
It's clear you expect a higher level but I hope you can trust me to improve with time.
If not it will be like failing the admission exams.What can i do? That's life...

No, you have it all wrong, I don't expect anything from you because I'm not a university. Posting a conceptual question is accepted in the quantum section of physics forums, but if you're going to keep on like this you should be posting here instead: https://www.physicsforums.com/forums/advanced-physics-homework.154/ . Now the misunderstanding is clear so this is my last post in this thread, the homework section is where you should post.
 
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  • #39
ddd123 said:
No, you have it all wrong, I don't expect anything from you because I'm not a university. Posting a conceptual question is accepted in the quantum section of physics forums, but if you're going to keep on like this you should be posting here instead: https://www.physicsforums.com/forums/advanced-physics-homework.154/ . Now the misunderstanding is clear so this is my last post in this thread, the homework section is where you should post.

I thank you for guiding me further to "homework PF"
By the way i am p 35.Thanks to your legitimate critics i made an extra effort and understood by my self the mathematics of the previous pages.
I found it relatively easy.So i am surely not as you say "going to keep on like this." I hope to satify the requirements necessary for getting the help i will need.Maybe some day i will be able to help others on my turn.
 
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