What's the role of "virtual particles" in quantum mechanics ?

Answer 1

Virtual particles are how quantum field theory manages to fit forces into a field picture. Forces--like the electromagnetic force which holds a magnet to a refrigerator door--are, in this formalism, mediated by the exchange of "virtual particles."

The value in this description is that, mathematically, the virtual particles have the same form as real particles--in the electromagnetic case, photons--which are visible excitations of the same field. So it unifies the force with the excitations in one neat theoretical description. The force, the light you see--all just photons.

What divides virtual particles from real ones is that real ones satisfy energy conservation conditions which allow them to propagate freely, essentially forever, whereas virtual particles can live only so long as the Heisenberg uncertainty principle allows. You might think of the force as the price the target pays for absorbing ("seeing") a virtual particle emitted from something else.

Answer 2

"Virtual" particles are mediating particles in interactions, such as photons in electron-electron scattering. Since they don't exist they do not have to be "on the mass shell" ie. they don't have to have the mass normally associated with such particles. They don't really exist, they're just useful in quantum field theory.

Answer 3

to make you ask questions : )