In summary, virtual particles are a mathematical concept used in quantum field theory, where they are represented as points in spacetime. They do not physically exist and must be removed by integration in calculations. In the coordinate-space representation, they appear on-mass-shell, but only 3-momentum is conserved at each vertex. In the momentum-space representation, they can be both on- and off-mass-shell, but 4-momentum is conserved at each vertex and loop. Virtual particles serve a purpose in calculations by allowing for negative dot products and can be compared to imaginary numbers in mathematics.
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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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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.
 
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FAQ: What are Virtual Particles? A 10 Minute Introduction

What are virtual particles?

Virtual particles are subatomic particles that appear and disappear in a vacuum due to the uncertainty principle in quantum mechanics. They are not considered to be real particles as they cannot be directly observed, but they play a crucial role in explaining the behavior of particles and forces in the universe.

How do virtual particles come into existence?

Virtual particles come into existence as a result of the constant fluctuation of the quantum vacuum. According to Heisenberg's uncertainty principle, energy can briefly fluctuate in a vacuum, creating pairs of particles and antiparticles that quickly annihilate each other.

Do virtual particles have mass?

Yes, virtual particles have mass, but it is usually much smaller than the mass of their corresponding real particles. This is because they only exist for a very short amount of time before annihilating, and their mass is determined by the uncertainty principle.

Can virtual particles be observed?

No, virtual particles cannot be observed directly. They can only be detected indirectly through their effects on observable particles. For example, the exchange of virtual particles is responsible for the forces between particles, such as the electromagnetic force.

Are virtual particles important in understanding the universe?

Yes, virtual particles are crucial in understanding the behavior of particles and forces in the universe. They play a significant role in the Standard Model of particle physics and have been confirmed through various experiments. Without the concept of virtual particles, our understanding of the fundamental workings of the universe would be incomplete.

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