Transformation of the affine connection

AI Thread Summary
The discussion revolves around understanding the transformation of the affine connection, specifically the meaning of "swapping derivatives with respect to a and x'" and how to derive equation 3.17. Participants express confusion about the generation of a minus sign during the process, even when applying chain rules and relabeling dummy indices. There is a call for clarification and assistance, as multiple users share similar difficulties with the concept. The need for a clearer explanation of the mathematical steps involved is emphasized. Overall, the thread highlights a collective struggle to grasp the transformation process in the context of affine connections.
ehrenfest
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Homework Statement


Can someone explain what they mean at the bottom of the page "by swapping derivatives with respect to a and x' " and in general how they arrived at equation 3.17?


Homework Equations





The Attempt at a Solution

 

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can people see the attachment okay?
 
anyone?
 
ehrenfest said:

Homework Statement


Can someone explain what they mean at the bottom of the page "by swapping derivatives with respect to a and x' " and in general how they arrived at equation 3.17?


Homework Equations





The Attempt at a Solution


I have to admit that I am a bit puzzled by this. I don't see how a minus sign may be generated even if one relabels the dummy indices, use the chain rules to go from x to c', etc. I must be missing something. I hope someone else can jump in.
 
I have the same problem, can anyone help us?
 
Thread 'Help with Time-Independent Perturbation Theory "Good" States Proof'

Thread 'Help with Time-Independent Perturbation Theory "Good" States Proof'

(Disclaimer: this is not a HW question. I am self-studying, and this felt like the type of question I've seen in this forum. If there is somewhere better for me to share this doubt, please let me know and I'll transfer it right away.) I am currently reviewing Chapter 7 of Introduction to QM by Griffiths. I have been stuck for an hour or so trying to understand the last paragraph of this proof (pls check the attached file). It claims that we can express Ψ_{γ}(0) as a linear combination of...
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