On tree level Feynman diagrams

In summary, the author is assured that scattering cross-sections in QFT computed at tree level correspond to cross-sections in the classical theory. However, he has two big misunderstandings that he would appreciate someone clearing up for him.
  • #1
metroplex021
151
0
Hi folks,

I'm assured that scattering cross-sections in QFT computed at tree level correspond to cross-sections in the classical theory. For example the tree level cross-section for electron-electron scaterring in QED corresponds to scattering of classical point charges. But I'm not sure I understand how this can be. In particular, I think I have two big misunderstandings and if anyone could set me straight I would be grateful!

Suppose we have an amplitude for 2-> 2 scattering, represented by A(p1,p2,q1,q2) where p1...qn encode the state-dependence and state-independent properties of the particles involved.

(1) Since inelastic processes -- by which I mean processes that change the kinds of particles involved -- are not allowed classically, I take it that the contribution from tree diagrams must be zero in these cases. But it doesn't seem to be the case that tree diagrams give zero in inelastic processes in QFT! Could someone tell me what the error is in my thought here?

(2) Since classical field theory is deterministic, it strikes me that the classical amplitude for anyone process must always be 1 or 0. But of course the sum of tree-level terms in a QFT is not always going to sum to either of these!

Can anyone help me interpret this supposed classical limit, because I'm clearly not getting this gist here at all? Thanks a lot!
 
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  • #2
Quantum theories correspond to classical theories in the so-called classical limit. Only in the cassical limit does (and should!) a quantum calculation agree with a classical calculation for some given process.
 
  • #3
For a quantum theory to be correct, any result obtained using classical theory must somehow be obtainable using the quantum description. In the case of scattering in QFT, classical results are produced at tree-level. However this doesn’t mean that all tree-level results can be obtained or understood classically. The classical and quantum concepts involved in the description of the same (or any) system are profoundly different with quantum theory giving a way to understand physics that is deeper and more general than the corresponding classical description of a given system. What you need to investigate is the precise correspondence between classical and quantum descriptions and in particular how a classical limit, when one exists, emerges from a quantum theory (sources for which abound).
 

1. What is a tree level Feynman diagram?

A tree level Feynman diagram is a graphical representation of a scattering process in particle physics, where the particles involved are interacting at the tree level, meaning they are not exchanging any virtual particles.

2. How are tree level Feynman diagrams used in particle physics?

Tree level Feynman diagrams are used to calculate the probability amplitudes for various scattering processes in particle physics. This is done by assigning mathematical expressions to each line and vertex in the diagram, and then combining them to obtain the overall amplitude.

3. What is the significance of tree level Feynman diagrams?

Tree level Feynman diagrams provide a visual representation of particle interactions and allow for calculations of scattering amplitudes in an intuitive way. They also help in understanding the underlying symmetries and conservation laws of particle interactions.

4. How do tree level Feynman diagrams differ from loop diagrams?

In contrast to tree level diagrams, loop diagrams involve the exchange of virtual particles and represent higher-order corrections to the tree level process. This makes them more complicated to calculate, but they are necessary for precise predictions in particle physics.

5. Can tree level Feynman diagrams be used to study the decay of particles?

Yes, tree level Feynman diagrams can be used to study the decay of particles, as the process can be represented as a scattering process between the initial and final states of the decaying particle. However, higher-order corrections may also need to be considered for more accurate predictions.

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