Abstract
We review the concept of purely virtual particle and its uses in quantum gravity, primordial cosmology and collider physics. The fake particle, or “fakeon”, which mediates interactions without appearing among the incoming and outgoing states, can be introduced by means of a new diagrammatics. The renormalization coincides with one of the parent Euclidean diagrammatics, while unitarity follows from spectral optical identities, which can be derived by means of algebraic operations. The classical limit of a theory of physical particles and fakeons is described by an ordinary Lagrangian plus Hermitian, micro acausal and micro nonlocal self-interactions. Quantum gravity propagates the graviton, a massive scalar field (the inflaton) and a massive spin-2 fakeon, and leads to a constrained primordial cosmology, which predicts the tensor-to-scalar ratio r in the window 0.4≲1000r≲3.5. The interpretation of inflation as a cosmic RG flow allows us to calculate the perturbation spectra to high orders in the presence of the Weyl squared term. In models of new physics beyond the standard model, fakeons evade various phenomenological bounds, because they are less constrained than normal particles. The resummation of self-energies reveals that it is impossible to get too close to the fakeon peak. The related peak uncertainty, equal to the fakeon width divided by 2, is expected to be observable.
Highlights
We review the concept of purely virtual particle and its uses in quantum gravity, primordial cosmology and collider physics
The renormalization coincides with one of the parent Euclidean diagrammatics, while unitarity follows from spectral optical identities, which can be derived by means of algebraic operations
Virtual particles have a variety of applications, which range from collider physics, to quantum gravity and primordial cosmology
Summary
Nature “is written in that great book which ever is before our eyes—I mean the universe—but we cannot understand it if we do not first learn the language and grasp the symbols in which it is written. The propagators of LW ghosts and purely virtual particles cannot, because the i and −i prescriptions cannot coexist inside Feynman diagrams without violating unitarity, the locality and Hermiticity of counterterms and stability [30]. These two options need suitable integration prescriptions or, in the case of fakeons, a new diagrammatics. The removal of degrees of freedom from the incoming and outgoing states is consistent only if it is compatible with unitarity, in which case it is called “projection” and the reduced action is called “projected action” This means that the Equation (3) holds in a subspace V of the total space W of states one uses to build the theory. The fakeon projection is compatible with unitarity order by order (and diagram by diagram) in the perturbative expansion [1]
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