# Lectures by Susskind versus Zee on the ${\rm SU}(5)$ grand unified theory notations

+ 3 like - 0 dislike
222 views

I was comparing two lectures about $${\rm SU}(5)$$ grand unified theory.

1. a lecture of Susskind He showed how to write $$(5 \times 5)_{asym}=\bar{10}$$ as

1. a lecture of Zee showed how to write $$(\bar 5 \times \bar 5)_{asym}={10}$$ as

Other than the difference between $$(5 \times 5)_{asym}=\bar{10} \text{ versus } (\bar 5 \times \bar 5)_{asym}={10}$$

My question is that there is also an extra minus sign in Zee's notation? See the $$- \bar u$$ in the 1st row and the 3rd column. I suppose Zee is correct and Susskind missed a minus sign or more signs. Am I understanding it correct?

This post imported from StackExchange Physics at 2020-11-28 23:05 (UTC), posted by SE-user annie marie heart
I should agree with you... Lenny is notoriously sloppy with signs and such... he is quick, and he assumes anyone can catch his trivial errors. In this case, the color subspace has a Levi-Civita $\epsilon_{rgb}$ structure, so, yes, you need - signs like Zee, or Langacker. People choose orderings and signs most convenient to them, but in the 3x3 color block you focus on, Lenny definitely needs some signs flipped.
 Please use answers only to (at least partly) answer questions. To comment, discuss, or ask for clarification, leave a comment instead. To mask links under text, please type your text, highlight it, and click the "link" button. You can then enter your link URL. Please consult the FAQ for as to how to format your post. This is the answer box; if you want to write a comment instead, please use the 'add comment' button. Live preview (may slow down editor)   Preview Your name to display (optional): Email me at this address if my answer is selected or commented on: Privacy: Your email address will only be used for sending these notifications. Anti-spam verification: If you are a human please identify the position of the character covered by the symbol $\varnothing$ in the following word:p$\hbar$ysicsOverflo$\varnothing$Then drag the red bullet below over the corresponding character of our banner. When you drop it there, the bullet changes to green (on slow internet connections after a few seconds). To avoid this verification in future, please log in or register.