# What do they mean with real and virtual corrections ?

• Sleuth
In summary, the real and virtual corrections always work together to give you finite results in perturbation theory. This is called the "KLN Theorem".
Sleuth
Hi guys,
it's been a long time since I wrote here the last time...

I come with a very stupid question... it's only a definition, and it's a matter of ignorance I know that... but nobody ever explained it to me, nor i ever found a clear definition on a QFT book... or probably I simply don't know where to look for it...

the question is, what do people mean with real and virtual corrections? When you compute a process in perturbative QFT i know that real particles are those which are on-shell, or those written as external lines, while virtual particles are the internal off-shell particles in a feynman diagram... but this only confuses me more... why when people talk about computing some process at some perturbative order, they always talk about virtual and real corrections? what's the difference? and what do they mean from a mathematica and mostly physical point of view?

thank you and sorry if this is too trivial,

Sleuth

Real corrections are corrections where the additional interactionvertex leads to the creation of a particle that survives, i.e. makes it out of the interaction.
Virtual corrections are when the additional particle is also absorbed.

As an example
if we have a e- and e+ going via a photon to mu- and mu+, a real correction can be that one of the muons send out a photon, so that we really have a process which create mu+, mu- and a photon. On the other hand, a virtual correction could be that the mu- sends out a photon that is absorbed by the mu+.

Does this make it clearer to you?

Hey, thank you so much :)
so it was just a name problem as i guessed :)

now it is perfectly clear...

Now I have a second question... Let's consider just QED for simplicity.

The 1 Loop vertex VIRTUAL correction should be the one which gives the famous \alpha/(2 \pi) by Schwinger (right?), while the REAL corrections are simply the Breemsstrahlung emission of a photon...

Now this is the question: the two corrections have to be summed to get rid of the IR soft and collinear divergences...

Is this always true? I mean, when dealing with any number of loops, is it always true that the divergences of the REAL corrections are canceled by those of the Virtual corrections?

Thank you

Sleuth

YES, real and virtual corrections always conspire to give you IR finite results, to all orders in perturbation theory. This is called the "KLN Theorem".

In practice this provides a powerful way you know you made a mistake: if you get an IR divergence in the final result, there are one of two possibilities: (1) you made a mistake in the calculation, or (2) you are asking the wrong question!

Possibility (2) is realized with the bremmstrahlung: if you try to ask, "What is the probability of emitting a single photon?" that makes no sense since you actually cannot observe the emission of a single photon with arbitrary energy. What you MEANT to ask is "What is the probability of emitting a single photon with enough energy for me to detect?" THAT is the correct question to ask! And QED has told you that the first question makes no sense by giving you an IR-divergent answer.

Thank you so much... I'm starting my studies on qcd now and it seems i had so many questions :P
but now things are going to the right place thanks to some calculations that I'm doing :)
thanks again
Sleuth

## 1. What are real and virtual corrections?

Real and virtual corrections are two types of calculations used in theoretical physics and computational science. Real corrections refer to the actual physical processes or phenomena being studied, while virtual corrections refer to mathematical corrections needed to account for the limitations of the theoretical model.

## 2. How do real and virtual corrections differ?

The main difference between real and virtual corrections lies in their physical nature. Real corrections involve the actual exchange of particles or energy in a physical system, while virtual corrections are mathematical constructs used to account for the effects of these interactions on the system being studied.

## 3. Why are real and virtual corrections important in scientific research?

Real and virtual corrections play a crucial role in scientific research as they help refine and improve our understanding of physical phenomena. By accounting for both real and virtual corrections, scientists are able to make more accurate predictions and better explain the behavior of complex systems.

## 4. Can you provide an example of real and virtual corrections in action?

Sure, a common example of real and virtual corrections is in the study of particle interactions in quantum field theory. Real corrections, such as particle scattering, involve the actual exchange of particles, while virtual corrections account for the effects of these interactions on the overall probability of the system.

## 5. How are real and virtual corrections calculated?

Real and virtual corrections are calculated using a combination of theoretical models and computational techniques. Real corrections can be calculated using experimental data and physical laws, while virtual corrections require advanced mathematical methods such as perturbation theory to account for their effects on the system being studied.

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