Abstract
We formulate quantum field theories of massive fields of arbitrary spins. The presence of both physical and fake particles, organized into multiplets, makes it possible to fulfill the requirements of locality, unitarity and renormalizability at the same time. The theories admit cubic and quartic self-interactions and can be coupled to quantum gravity and gauge fields. The simplest irreducible bosonic and fermionic multiplets are made of towers of alternating physical and fake particles. Their mass spectrum is constrained by RG invariant relations and depends on just one or two masses. The fixed points of the renormalization-group flow are scale invariant, but not necessarily conformal invariant. The Palatini version of quantum gravity with fakeons is equivalent to the non-Palatini one coupled to a peculiar multiplet of order 3. As a consequence, it is equally renormalizable and unitary.
Highlights
Of “fakeon” [15], that is to say, a fake particle that mediates interactions, but does not belong to the spectrum of asymptotic states
The good news are that the calculations of Feynman diagrams with the fakeon prescription in quantum gravity [21, 22] are no harder than analogous calculations in the standard model
The models built along this guideline uncover a hidden subsector of quantum field theory
Summary
We study the bosonic multiplets, starting from the order-1 field χμ. The unique two-derivative local Lagrangian we can write for it is. The no-tachyon condition gives a1 > −1 When it holds, the pole at p2 = m21 has a residue with the correct sign for a physical particle, while the pole at p2 = m20 has a residue with the wrong sign. If the overall sign of (2.1) is flipped, the roles of the two poles are exchanged and we obtain a multiplet made of a fake vector and a physical scalar. Summarizing, with the conventions stated above the massive vector χμ describes a multiplet made of a spin-1 physical particle and a spin-0 fakeon. The fakeon prescription in (2.7) just refers to the p2 = m21 pole, while it is understood that the spurious poles at p2 = 0 are defined by means of the Feynman prescription. Summarizing, the order-2 massive field χμν describes a multiplet made of a spin-2 particle, a spin-1 fakeon and a spin-0 particle
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