Ax 4 in page 19 of Ticciati's QFT textbook.

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In summary, Ax 4 is the fourth component of the axial vector in quantum field theory (QFT), which is used to describe particle behavior and interactions. It is calculated using QFT's mathematical framework and is significant in understanding symmetries, conservation laws, and particle properties. Ax 4 can have a negative value as it is described by quantum states, and it is one of the four components that make up the axial vector.
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The axiom says:
"The interaction between two observations is constrained by causality
[tex]|x-y|^2 <0 \Rightarrow [\phi(x),\phi(y)]=0[/tex]
"

But |x-y|^2<0 is always false that means the if the condition applies then by simple logic the consequnet of the condition can occur or not occur, I don't understand this.
 
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The statement is about a timelike distance four-vector in Minkowski space. Its squared length is negative in the case of a -+++ metric.
 

Related to Ax 4 in page 19 of Ticciati's QFT textbook.

1. What is Ax 4 in page 19 of Ticciati's QFT textbook?

Ax 4 refers to the fourth component of the axial vector, which is a mathematical quantity used in quantum field theory (QFT) to describe the behavior of particles and their interactions.

2. How is Ax 4 calculated?

Ax 4 is calculated using the mathematical framework of QFT, which involves applying operators to quantum fields to obtain observables and calculate their values.

3. What is the significance of Ax 4 in QFT?

Ax 4, along with the other components of the axial vector, is important in understanding the symmetries and conservation laws of a system in QFT. It also plays a role in determining the properties and interactions of particles.

4. Can Ax 4 have a negative value?

Yes, Ax 4 can have a negative value. In QFT, the values of physical quantities are described by quantum states, which can have both positive and negative components.

5. How does Ax 4 relate to other components of the axial vector?

Ax 4 is one of the four components of the axial vector, along with Ax 1, Ax 2, and Ax 3. Together, these components form a four-dimensional mathematical object that describes the chirality (handedness) of a particle and its interactions with other particles.

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