The quest for purely virtual quanta: fakeons versus Feynman-Wheeler particles

Understand

The search for purely virtual quanta has attracted interest in the past.

• We consider various proposals and compare them to the concept of fake particle, or "fakeon".
• In particular, the Feynman-Wheeler propagator, which amounts to using the Cauchy principal value inside Feynman diagrams, violates renormalizability, unitarity and stability, due to the coexistence of the prescriptions $\pm i\epsilon $.
• We contrast the Feynman, fakeon and Feynman-Wheeler prescriptions in ordinary as well as cut diagrams.