Problem with Feynman's iε prescription

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In summary, The Feynman iε prescription is a technique used to solve integrals with singularities by displacing the energy variable by a small imaginary number iε. This choice of the sign of iε ensures that the propagator propagates into the future, preserving causality.
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alfredoalfred
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Homework Statement



My Problem is with Feynman's iε prescription. Trying to solve an Integral, it happens that there is a singularity s on the way. s depends on the Energy E of a particle. This integral is not convergent and doenst make any sense. To solve this Problem, one displaces the Energie from E to E - iε, with ε being very small. ( In Case of an anti particle it is E + iε).

Homework Equations



So the denominator of the dr integral looks like this: [ sqrt(r) - sqrt(2*(M-E' ) ] . now r gets integrated in such a way, that it always would hit the singularity s=sqrt(2*(M-E')). Changing E to E-iε however gets rid of the singularity. My problem is now not how to solve the Integral with the iε (which I am glad i found out already by myself), but to argue why we need such an iε in there in the first place.

The Attempt at a Solution



I tried to look up several books in Quantum field theory , but as i haven't taken such a course yet i don't understand them very well. There is so much stuff in there that I am not really sure I am missed an explanation. I am very confused :( .

Can you help to help me and give me a tip where i can find anything that explains it in maybe not a rigourous way? Trying to google feynman iε prescription has not really helped me :(

thank you very much for reading and maybe answering :)
 
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  • #2
The short answer is that the choice of the sign of i*epsilon determines whether you have chosen a propagator that propagates into the past or propagates into the future. For causalities sake you want the latter.
 

FAQ: Problem with Feynman's iε prescription

1. What is Feynman's iε prescription?

Feynman's iε prescription is a mathematical technique used in quantum field theory to deal with the problem of divergent integrals. It involves adding a small imaginary number, ε, to the denominator of the integral and then taking the limit as ε approaches 0.

2. Why is there a problem with Feynman's iε prescription?

The problem with Feynman's iε prescription is that it can lead to inconsistent and non-physical results. This is because it ignores the renormalization process, which is essential for removing the infinities in quantum field theory calculations.

3. How does the problem with Feynman's iε prescription affect our understanding of quantum field theory?

The problem with Feynman's iε prescription highlights the need for a more rigorous mathematical framework in quantum field theory. It also raises questions about the validity of certain calculations and the interpretation of physical results.

4. Are there alternative methods to deal with the divergent integrals in quantum field theory?

Yes, there are alternative methods such as dimensional regularization and lattice regularization that can also be used to deal with the divergent integrals in quantum field theory. These methods do not rely on Feynman's iε prescription and are more mathematically sound.

5. How can we address the problem with Feynman's iε prescription?

One way to address the problem with Feynman's iε prescription is to incorporate renormalization into the calculations, which involves removing the infinities in a more systematic and consistent manner. Another approach is to use alternative methods, as mentioned in the previous answer. Additionally, ongoing research and developments in quantum field theory are continuously seeking to improve our understanding and techniques in dealing with these types of problems.

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