The CPT theorem in Weinberg Book, Vol I

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I have been following Winberg Book, volume I.
I am currently working on chapter 5.8, the CPT theorem.

I have two questions in this chapter.

First one is, why can we choose the phases so that all particles
[itex] \zeta \xi \eta = 1 [/itex]
I tried to solve this problem by assuming that this is possible because [itex]\zeta[/itex] (intrinsic time reversal factor)has no physics significance and we can determine it arbitrarily. But, I am not sure whether this is true.
If my assumption is true, then we can do the same thing to PT or CT transformation, can't we?

Second one is, at the end of Pg 245, Weinberg said "A Hermitian scalar interaction density H(x) must be formed from tensors with an even total number of spacetime indices".
Is the reason that to make H(x) scalar, we have to make all spacetime indices be contracted to one another. But, I am not sure my argument here is right, either.

Thank you.
 

Answers and Replies

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Bill_K
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First one is, why can we choose the phases so that all particles ζξη=1
For example for a scalar field φ(x), if you change it by a constant phase, φ(x) → eφ(x), then by (5.8.1), ζξη → e2iα ζξη. So you can choose α to make ζξη real and positive.
 

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