Quantum field theories of arbitrary-spin massive multiplets and Palatini quantum gravity

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.

Ghost and Tachyon Free Propagation up to spin-3 in Lorentz Invariant Field Theories

“…we find, as common when spin sectors stem from the same field, that is impossible to simultaneously require causality and unitarity for both (see also [45]). We solve this by requiring a 7 = −1 , m 2 1 > 0 and a 3 = 3 .…”

Purely virtual particles versus Lee-Wick ghosts: physical Pauli-Villars fields, finite QED and quantum gravity

“…It is possible to have renormalizability (and unitarity) if we replace Ω µν with a whole massive spin 2 multiplet Υ µν , of the type studied in ref. [15]. In that case Υ µν is a symmetric, traceless tensor and contains a triplet: the spin 2 particle Ω µν , a spin 1 fakeon Ω µ and a massive scalar Ω.…”

“…However, a number of unresolved issues with general covariance (and gauge invariance) show that it cannot be applied to gravity as is. A covariant decomposition can be achieved by adding a massive spin 2 multiplet (which can be done in a unitary and renormalizable way as explained in [15]). However, this procedure just gives the theory of [10] coupled to matter in a peculiar way.…”

Purely Virtual Particles in Quantum Gravity, Inflationary Cosmology and Collider Physics

“…It is also possible [14,15] to avoid certain troubles of the Lee-Wick models [16][17][18][19][20][21] by switching to theories of particles and fakeons. Finally, the fakeon prescription can be used to give sense to higher-spin massive multiplets [22]. Coupled to gravity, higher-spin massive multiples change the ultraviolet behavior and open the way to asymptotic freedom [23].…”