Sign confusions on CFT (yellow book) Page 29

  • Thread starter ivantheczar
  • Start date
  • Tags
    Book Sign
In summary, there is a discrepancy in the derivation of the propagator kernel in the book Conformal Field Theory by Francesco, Mathieu, and Senechal. The signs on the first and second line of equation (2.73) do not match, which makes it difficult to identify the term with the derivatives. Despite checking the properties of the coherent states, no solution to this sign issue was found. The errata for the book does not mention this issue, but it is possible that there should be a negative sign in the exponent in equation (2.69c). This can be compared to Fradkin's notes on the same topic.
  • #1
ivantheczar
1
0
On the book Conformal Field Theory by Francesco, Mathieu and Senechal (the yellow book), in the derivation of the propagator kernel [itex]K(\delta t,\xi,\xi')[/itex] on (2.73), the signs on the first and second line just doesn't match.

On first line it has [itex]-\xi^+ T \xi'-{\xi'}^+ T \xi' [/itex] while the second line, after simplifying, has [itex]\xi^+ T \xi'-{\xi'}^+ T \xi' [/itex], which is necessary to identify the term with the derivatives.

However, tracing back up to the definition of the properties of the coherent states, I cannot find any way to fix this sign. Does anyone has encounter this part and have a solution?

(For those without the book, the page is attached)
 

Attachments

  • page29.jpg
    page29.jpg
    76.1 KB · Views: 339
Physics news on Phys.org
  • #2
It is not mentioned in the errata (for future reference, it is found at http://www.physique.usherbrooke.ca/pages/senechal/cft ), however I wonder if there really should be a negative sign in the exponent in eq. (2.69c). I don't have time to check it carefully now, but compare, for example, Fradkin's notes: http://webusers.physics.illinois.edu/~efradkin/phys582/582-chapter8.pdf
 
Last edited by a moderator:

1. What is CFT and why is it important?

CFT stands for Conformal Field Theory, which is a mathematical framework used to describe the behavior of quantum fields. It is important because it has applications in many areas of physics, such as string theory and condensed matter physics.

2. What are sign confusions and why do they occur on page 29 of the yellow book?

Sign confusions refer to errors in the signs of certain equations or terms in a mathematical expression. On page 29 of the yellow book, these confusions occur due to a convention used for the conformal transformation, which can be confusing for some readers.

3. How can sign confusions on page 29 of the yellow book be resolved?

The best way to resolve sign confusions is to carefully check the signs in the equations and make sure they are consistent with the underlying mathematical principles. It may also be helpful to consult other resources or seek clarification from experts in the field.

4. Are sign confusions on page 29 of the yellow book a common issue?

Yes, sign confusions can be a common issue in mathematical literature, especially in more complex theories like CFT. It is important to carefully review and verify the signs in equations to avoid any misunderstandings or errors.

5. How can I prevent sign confusions while studying CFT?

To prevent sign confusions, it is important to have a strong understanding of the underlying mathematical principles and conventions used in CFT. It can also be helpful to double check equations and consult with other resources or experts if needed.

Similar threads

  • Differential Geometry
Replies
14
Views
2K
  • Beyond the Standard Models
Replies
1
Views
2K
Replies
11
Views
2K
  • Special and General Relativity
Replies
7
Views
1K
  • Math Proof Training and Practice
2
Replies
48
Views
8K
  • Special and General Relativity
Replies
11
Views
2K
  • Science and Math Textbooks
Replies
2
Views
4K
  • Advanced Physics Homework Help
Replies
3
Views
944
  • Advanced Physics Homework Help
Replies
5
Views
3K
  • Special and General Relativity
3
Replies
78
Views
4K
Back
Top