Mathematical Quantum Field Theory - Symmetries - Comments

In summary: Thanks!I have fixed the first two. I haven't gotten around writing an exposition of the Dickey bracket (maybe later when I find the time), but I have at least changed the link so that it points more manifestly to the commented list of references: here.In summary, the author provides a summary of the content.
  • #1
Urs Schreiber
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Greg Bernhardt submitted a new PF Insights post

Mathematical Quantum Field Theory - Symmetries
qtf_symmerities.png


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Great read.

Glad you mentioned the Erlanger program - I sometimes do but I thought I was the only one that recognized its importance to modern physics.

Thank's again for penning this very interesting series - I am learning and/or revising a lot.

Thanks
Bill
 
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  • #3
In Defn 6.12, eq(63): non-rendering latex
 
  • #5
eltodesukane said:
unable to load the page properly
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many equations, like (60), do not display
Hmm. All equations except (63) display ok for me. Your problems with the others might be a consequence of not being able to load the page properly. (Are you using a script-blocker, such as NoScript?)

It's probably better to leave comments here in this thread.
 
  • #6
strangerep said:
In Defn 6.12, eq(63): non-rendering latex

Thanks. I had seen this, but it took me a while to understand the problem, since after isolating the relevant code it rendered properly. Turns out the problem was just a duplication of the equation label.

I have fixed it now.

Due to the additions that I made in the previous chapter, regarding the presymplectic current, which we discussed, the equation numbering here got shifted. What used to be (63) is now (67).
 
  • #7
strangerep said:
Hmm. All equations except (63) display ok for me. Your problems with the others might be a consequence of not being able to load the page properly. (Are you using a script-blocker, such as NoScript?)

It's probably better to leave comments here in this thread.
Maybe the OP is using the mobile app. At least under Android it hasn't worked too well the last time I tried it. It's working all fine under linux (using firefox) as well as under Android (using the chrome browser or also firefox). I guess it should also work under Windows as far as one can say that anything works there ;-).
 
  • #8
vanhees71 said:
Maybe the OP is using the mobile app. At least under Android it hasn't worked too well the last time I tried it.

That's interesting. Do we know the relevant developer forum where this issue could be brought to attention? Somebody might want to go and try to fix it.
 
  • #9
- "In Phase space below" should have a lower case P.
- "the following definition 6.2 of evolutionary vector fields we follow remark 4.10 saying" has two spurious line breaks
- You refer to https://ncatlab.org/nlab/show/conserved+current for the Dickey Lie bracket, but while it is mentioned there, it is not defined there.
 
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  • #10
A. Neumaier said:
- "In Phase space below" should have a lower case P.
- "the following definition 6.2 of evolutionary vector fields we follow remark 4.10 saying" has two spurious line breaks
- You refer to https://ncatlab.org/nlab/show/conserved+current for the Dickey Lie bracket, but while it is mentioned there, it is not defined there.

Thanks!

I have fixed the first two. I haven't gotten around writing an exposition of the Dickey bracket (maybe later when I find the time), but I have at least changed the link so that it points more manifestly to the commented list of references: here
 
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1. What is mathematical quantum field theory?

Mathematical quantum field theory is a branch of theoretical physics that uses mathematical methods to study quantum field theories, which describe the interactions of elementary particles and their quantum properties.

2. What are symmetries in quantum field theory?

Symmetries in quantum field theory refer to the invariance of physical laws and equations under certain transformations, such as rotations, translations, and gauge transformations. These symmetries play a crucial role in understanding the behavior of quantum fields.

3. How do symmetries impact quantum field theory?

Symmetries in quantum field theory are essential for understanding and predicting the behavior of particles and their interactions. They allow us to make predictions about the behavior of quantum fields and their properties, such as energy and momentum.

4. Can symmetries be broken in quantum field theory?

Yes, symmetries can be broken in quantum field theory. This occurs when the physical system does not exhibit the same symmetries as the mathematical equations that describe it. This phenomenon is known as spontaneous symmetry breaking and is an important concept in understanding the behavior of particles in the universe.

5. What are some applications of quantum field theory?

Quantum field theory has many applications in theoretical physics, including the study of high-energy particle physics, cosmology, and condensed matter physics. It also has practical applications in technologies such as quantum computing and quantum information processing.

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