Applying LSZ reduction - scattering particles

May 9, 2019

binbagsss

Homework Statement: Hiyah

I was initially confused about which way to choose the sign of the momentum , since it gives arise to different exponential ^ momentum combinations and thus different deltas for the momentum conservation . I came to conclusion that it doesn’t matter as long as you are consistent . ( which I found this I Be correct when I came across this https://physics.stackexchange.com/questions/452539/sign-ambiguity-when-going-from-position-to-momentum-space-evaluating-feynman-dia# ).

My question , pretty much , is the definition of consistency here . There are two things to consider I believe :

1) having some consistent pattern to which external vertices you point toward a vertex, and which away from a vertex .

2) what system you choose to denote positive and negative to : I.e right and left , up and down, or into a vertex and out of a vertex.

My choice I like to use is :
1) all point in the same direction - eg right
2) + or - given by whether in to a vertex or out

My question is are my 1) and 2) which I talk about for consistency correct ? E.g is it even correct to consider you may denote plus or minus by left / right or should it always be into and out of a vertex, regarding number 1, I feel as though the easier option is to label everything in same direction , but say I am considering variations of a diagram by keeping the external points fixed (1,2,3,4) - I believe another way of consistency woulda be to always associate the same direction with the same external point - these could be all the same , three same , one not , two-two - it does not Matter . Am I correct in thinking this is a ‘ valid move ‘ ?

Many thanks !

Relevant Equations: Above

Above

May 9, 2019

Nate810

the archesAbove the arches of a bridge is typically where the roadway is located. This area of the bridge spans the gap between the two sides and is supported by the arches beneath it. The arches are typically made of stone, brick, or concrete and are designed to distribute the weight of the bridge across the entire span.

1. What is LSZ reduction and how does it relate to scattering particles?

LSZ reduction is a mathematical technique used in quantum field theory to calculate scattering amplitudes, which describe the probability of particles interacting and changing direction. It relates to scattering particles by providing a way to calculate these amplitudes in terms of the fields that describe the particles.

3. What is the significance of LSZ reduction in quantum theory?

LSZ reduction is significant in quantum theory because it allows for the calculation of scattering amplitudes, which are crucial in understanding the behavior of particles at the quantum level. It also provides a way to connect the mathematical framework of quantum field theory with experimental results.

4. What are the limitations of LSZ reduction?

One limitation of LSZ reduction is that it only applies to free particles, meaning particles that do not interact with each other. It also assumes that the particles are stable, which is not always the case in reality. Additionally, LSZ reduction can become more complicated when dealing with particles with spin or in theories with interactions.

5. How does LSZ reduction contribute to our understanding of quantum theory?

LSZ reduction contributes to our understanding of quantum theory by providing a way to calculate scattering amplitudes, which are crucial in predicting and understanding the behavior of particles at the quantum level. It also connects the theoretical framework of quantum field theory with experimental results, allowing for the validation of the theory.