The CPT theorem in Weinberg Book, Vol I

In summary: 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".This is because in a Hermitian scalar field theory, the field and its conjugate must have the same transformation properties under Lorentz transformations. Therefore, the interaction density must also have an even number of spacetime indices to maintain this symmetry.
  • #1
wphysics
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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.
 
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  • #2
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) → eiαφ(x), then by (5.8.1), ζξη → e2iα ζξη. So you can choose α to make ζξη real and positive.
 

Related to The CPT theorem in Weinberg Book, Vol I

1. What is the CPT theorem in Weinberg Book, Vol I?

The CPT theorem, also known as the charge-parity-time reversal theorem, states that in a quantum field theory, the combined operation of charge conjugation (C), parity transformation (P), and time reversal (T) must leave the theory invariant. This means that if a physical process occurs in a certain way, then the mirror image of that process occurring in reverse time with opposite charges must also be allowed by the theory.

2. Why is the CPT theorem important in physics?

The CPT theorem is important because it is a fundamental symmetry of the laws of physics. It implies that for every physical process that we observe, there must exist a corresponding antiprocess with opposite charges and reversed time direction. This symmetry has been extensively tested and is a cornerstone of many theories in particle physics and cosmology.

3. What evidence supports the CPT theorem?

The CPT theorem has been supported by numerous experimental observations, such as the decay of neutral K-mesons and the behavior of matter and antimatter in particle accelerators. Additionally, the consistency of the Standard Model of particle physics, which is based on the CPT symmetry, provides further evidence for the validity of the theorem.

4. How does the CPT theorem relate to the concept of antimatter?

The CPT theorem predicts that antimatter must have the opposite charge, parity, and time direction compared to its corresponding matter particle. This means that if a particle and its antiparticle were to collide, they would annihilate and produce pure energy. The existence of antimatter has been confirmed in experiments, providing further support for the CPT theorem.

5. Are there any exceptions to the CPT theorem?

There are some theoretical models, such as string theory, that suggest violations of the CPT symmetry under certain extreme conditions. However, these violations have not been observed in experiments and are still a subject of ongoing research. In general, the CPT theorem is considered to be a fundamental principle of physics that holds true in almost all cases.

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