Is Feynman's time-ordering prescription covariant?

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In summary, the conversation discusses the relationship between time-ordering and the choice of Lorentz frame, specifically in regards to the S-matrix theory and its covariance. It is suggested that the time-ordering prescription is implicitly defined for each Lorentz frame, and that Lorentz boosts may affect the ordering of operators. The S-matrix is described as unitary and unaffected by time ordering, and a covariant theory is proposed in the path integral approach. Further reference is given in Landau & Lif****z's Quantum Electrodynamics.
  • #1
Cinquero
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We all know that time-ordering depends on the choice of Lorentz frame. So my question is somewhat obvious...

Please give me a hint on where to look up that problem, eg. why the S-matrix theory is covariant.

I guess the time-ordering prescription is implicitly defined for each single Lorentz frame (relative times are specific to each frame), and therefore we'll have to adjust the ordering of the operators when applying Lorentz boosts -- thereby rendering the theory covariant in an obvious way. Is that correct?
 
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  • #2
By definition,the S matrix is both unitary and has no problem with the time ordering.A covariant theory of the S matrix is given in the path integral approach,which,as you might know,is much simpler.

Daniel.
 
  • #3
The derivation (along with the reason for invariance) is given in Landau & Lif****z's Quantum Electrodynamics, p. 283-286, if the OP wants further reference.
 

1. What is Feynman's time-ordering prescription?

Feynman's time-ordering prescription is a mathematical technique used in quantum field theory to properly order time-dependent operators in equations. It is used to calculate the probability amplitudes of particle interactions in quantum field theory.

2. Is Feynman's time-ordering prescription a covariant method?

Yes, Feynman's time-ordering prescription is covariant, meaning it is valid in all reference frames. This is because it follows the principles of special relativity and does not depend on a specific frame of reference.

3. Why is it important for Feynman's time-ordering prescription to be covariant?

It is important for Feynman's time-ordering prescription to be covariant because it allows for a consistent and accurate description of particle interactions in all reference frames. This is necessary in order to make accurate predictions and calculations in quantum field theory.

4. How does Feynman's time-ordering prescription ensure covariance?

Feynman's time-ordering prescription ensures covariance by using the Minkowski metric, which is a mathematical tool that allows for the description of physical phenomena in a way that is consistent with special relativity. By using this metric, the time-ordering prescription is able to remain valid in all reference frames.

5. Are there any limitations to Feynman's time-ordering prescription?

While Feynman's time-ordering prescription is a powerful tool in quantum field theory, it does have some limitations. It is not applicable to all quantum field theories, and it also does not take into account certain effects, such as non-local interactions. Additionally, it can become mathematically complex and difficult to work with in certain situations.

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