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Maybe someone reading this can enlighten me on the utility of thinking about virtual particles in the vacuum. This is not related that directly to the article,

by gpsx 10y ago

Maybe someone reading this can enlighten me on the utility of thinking about virtual particles in the vacuum. This is not related that directly to the article, but it is mentioned in it. Feynman diagrams are a perturbation theory expanding around a problem we can solve - non-interacting free fields. The lines in the diagram represent the particles in the free theory, not the interacting theory. Renormalization does allow us to make some correspondence between the two, but that can only be taken so far, at least to my understanding. (And perhaps this is my limitation.) There are lots of vacuum diagrams, for example. These represent the difference between the vacuum in the free theory and the interacting theory. That does not mean there is frothing going on in the interacting theory that is not in the free theory. The vacuum wave function is still a combination of field configurations each with an associated amplitude density. (And, relating to the article, of course, this creates an associated non-zero vacuum energy.) It looks just like the vacuum in a particle Schroedinger equation model, but just a lot more degrees of freedom. What are the virtual particles? I'd appreciate if someone could explain what people mean and why when they talk about these.

KenoFischer 10y ago
There is many ways to think about virtual particles. From a particle point of view one can think of it as quantum mechanics allowing you to create a high energy particle for a short amount of time, even if that would not be allowed classically. From a field theory point of view, you can have excitations in the fields that are not sufficient to be a particle, but can still interact locally.
- gpsx 10y ago
  I was looking for an explanation of why the lines of a Feynman diagram are called virtual particles when they are really particles in the unperterbed (or free) model. So why do you think of this as creation of a particle for a short amount of time?
  - KenoFischer 10y ago
    Generally if you look at the Feynman diagram for an interaction, you'll have some number of external legs which one thinks of as physical particles, as well as a number of interactions. The lines between the interactions may be particles whose mass exceeds the total amount of energy of the incoming particles, so they obviously can't be real. They are thus generally called virtual (or off-shell particles). How one can think of this is what I tried to address in the original response.
    - gpsx 10y ago
      I appreciate you saying the external legs can be thought of as physical particles, since they are not technically physical particles. The renormalization groups tells us that those look like physical particles. Internally to the interaction this is not true, which is why they would be called virtual particles. But I see them as a pure mathematical relic of the perturbation calculation. Perhaps I am just not able to extend my intuition here. And likely a more depth description from you or someone else is not really practical here. I just come back to the fact that in the end, particles are just different excitation states of the system. There is a vacuum state, a bunch of states we would consider one particle states, a bunch more we would consider two particle state, and so on. Doesn't this cover all configurations of the system and there are no "in-between" or what you would call off-shell states? I think these only make sense when we are making an approximation around the non-interactive model.
cft 10y ago
The external legs (propagators) of Feynman diagrams represent real (not virtual) particles, whose interactions we want to study. Virtual particles run in the closed loops of Feynman diagrams, i.e. they can be thought of as actual particles (of the same or of other types), being created by the collision of the real particles, and they recombine back into the real particles. So say two real particles collide and scatter off each other: the collision creates all kinds of "virtual particles" that are allowed by the interaction terms in the theory Lagrangian, and they recombine back into the same two real particles because of the same interaction terms. Using the famous Feynman's path integral, you integrate over all possible virtual particles and their states (with different contributions to the integral), normalize those contributions, and then you get the probability (or amplitude) of the real particles with a certain state getting scattered (or transitioning to "another [quantum] state") - the external incoming and outgoing "legs" of the diagram.

by gpsx 10y ago

KenoFischer 10y ago

There is many ways to think about virtual particles. From a particle point of view one can think of it as quantum mechanics allowing you to create a high energy particle for a short amount of time, even if that would not be allowed classically. From a field theory point of view, you can have excitations in the fields that are not sufficient to be a particle, but can still interact locally.

gpsx 10y ago
I was looking for an explanation of why the lines of a Feynman diagram are called virtual particles when they are really particles in the unperterbed (or free) model. So why do you think of this as creation of a particle for a short amount of time?
- KenoFischer 10y ago
  Generally if you look at the Feynman diagram for an interaction, you'll have some number of external legs which one thinks of as physical particles, as well as a number of interactions. The lines between the interactions may be particles whose mass exceeds the total amount of energy of the incoming particles, so they obviously can't be real. They are thus generally called virtual (or off-shell particles). How one can think of this is what I tried to address in the original response.
  - gpsx 10y ago
    I appreciate you saying the external legs can be thought of as physical particles, since they are not technically physical particles. The renormalization groups tells us that those look like physical particles. Internally to the interaction this is not true, which is why they would be called virtual particles. But I see them as a pure mathematical relic of the perturbation calculation. Perhaps I am just not able to extend my intuition here. And likely a more depth description from you or someone else is not really practical here. I just come back to the fact that in the end, particles are just different excitation states of the system. There is a vacuum state, a bunch of states we would consider one particle states, a bunch more we would consider two particle state, and so on. Doesn't this cover all configurations of the system and there are no "in-between" or what you would call off-shell states? I think these only make sense when we are making an approximation around the non-interactive model.

cft 10y ago

The external legs (propagators) of Feynman diagrams represent real (not virtual) particles, whose interactions we want to study. Virtual particles run in the closed loops of Feynman diagrams, i.e. they can be thought of as actual particles (of the same or of other types), being created by the collision of the real particles, and they recombine back into the real particles. So say two real particles collide and scatter off each other: the collision creates all kinds of "virtual particles" that are allowed by the interaction terms in the theory Lagrangian, and they recombine back into the same two real particles because of the same interaction terms. Using the famous Feynman's path integral, you integrate over all possible virtual particles and their states (with different contributions to the integral), normalize those contributions, and then you get the probability (or amplitude) of the real particles with a certain state getting scattered (or transitioning to "another [quantum] state") - the external incoming and outgoing "legs" of the diagram.