- #1
Peskin's Introduction to QFT 3.82 - What Has He Done?
- Context: Graduate
- Thread starter sunkesheng
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- Introduction Qft
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Discussion Overview
The discussion revolves around a specific section (3.82) of Peskin's Introduction to Quantum Field Theory (QFT), focusing on the manipulation and properties of matrices, particularly the Pauli matrices and Dirac indices. Participants are attempting to clarify the transformations and relationships between different entries in the matrices presented in the text.
Discussion Character
- Technical explanation
- Mathematical reasoning
- Debate/contested
Main Points Raised
- Some participants express confusion regarding the transformation of the indices in the matrices, particularly the change from \(\beta\) to \(\delta\) in the Pauli matrices.
- Others suggest writing out the components of each entry in the matrices to clarify the relationships and transformations involved.
- One participant notes the importance of explicitly writing out Dirac indices to understand the changes better.
- There is a mention of a realization regarding the relationship \(\sigma^{\mu}_{\alpha\beta}=\sigma^{\mu}^{T}_{\beta\alpha}\), indicating a significant insight into the properties of the matrices.
- Some participants express frustration with the notation used by Peskin, particularly the use of Greek letters for Dirac indices, which they find confusing.
Areas of Agreement / Disagreement
Participants appear to be engaged in a collaborative exploration of the topic, with some expressing confusion and others providing clarifications. There is no clear consensus on the best approach to understand the transformations, as different viewpoints and methods are presented.
Contextual Notes
Limitations include potential misunderstandings of the notation and transformations involved, as well as the reliance on specific definitions of the matrices and indices that may not be universally agreed upon.
- #2
ansgar
- 514
- 1
write out the components of each entry in the matrices
- #3
sunkesheng
- 10
- 0
i see ,but why the \singma[\nu]\sigma[\lambta] in the first row can be write to that in the second row,ansgar said:
- #4
ansgar
- 514
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what properties of the sigma can u think of?
- #5
sunkesheng
- 10
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many thanks .it is my fault,i don`t express my question clearly,soansgar said:
sigma is the 2*2 pauli matrix ,but subscript of the front two sigma matrixs in the first row is \beta ,in the second it changes to \delta,that is what i puzzled.
- #6
ansgar
- 514
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just write out every dirac index and massage it
- #7
sunkesheng
- 10
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ansgar said:
get it ,there is a change which is important and very simple ,and it is until now that i realized it :\sigma^{\mu}_{\alpha\beta}=\sigma^{\mu}^{T}_{\beta\alpha}
thanks a lot!
- #8
ansgar
- 514
- 1
ah great, I was about to do this all for myself so that I could pin-point exactly what is going on ;)
It "always" work to write out the Dirac indices
One thing I don't like is that Peskin uses greek letter for Dirac index sometimes.. like here, very annoying and confusing
It "always" work to write out the Dirac indices
One thing I don't like is that Peskin uses greek letter for Dirac index sometimes.. like here, very annoying and confusing
- #9
oopsitbroke
- 1
- 0
For posterity, here's a step-by-step derivation of line 1 to line 2 of eqn. 3.82 for Peskin & Schroeder QFT.
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