What are Virtual Particles? A 10 Minute Introduction

[Greg Bernhardt]

Definition/Summary
Virtual particles are a mathematical device used in perturbation expansions of the S-operator (transition matrix) of interaction in quantum field theory.
No virtual particle physically appears in the interaction: all possible virtual particles, and their antiparticles, occur equally and together in the mathematics and must be removed by integration over the values of their momenta.
In the coordinate-space representation of a Feynman diagram, the virtual particles are on-mass-shell (realistic), but only 3-momentum is conserved at each vertex, not 4-momentum, so there is no immediate way of obtaining 4-momentum-conserving delta functions.
In the momentum-space representation, the virtual particles are both on- and off-mass-shell (unrealistic), but 4-momentum is conserved at each vertex, and also round each loop (as shown by a delta function for each).
In the coordinate-space representation, each virtual particle appears “as itself”, but in the momentum-space...

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[HappyS5]

Hello,

I have a really basic question. I read the criteria that "see Weinberg, (3.5.13-14)" refers to, and to me, it seems that the equation will always be greater than 0 since it is squared. If so, what is it's purpose?

Source https://www.physicsforums.com/insig...xDDoRPVpOuw_A-k87PlyC1y6HrQqbcqTcgisJhA8Logn4

 

[mfb]

These are points in spacetime where the dot product of their difference doesn't have to be positive.

Not exactly the same, but you can compare this to the square of an imaginary number - it is negative, too.