Quantum gravity
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.
J. High Energy Phys. 07 (2020) 176 | DOI: 10.1007/JHEP07(2020)176
We derive the predictions of quantum gravity with fakeons on the amplitudes and spectral indices of the scalar and tensor fluctuations in inflationary cosmology. The action is $R+R^{2}$ plus the Weyl-squared term. The ghost is eliminated by turning it into a fakeon, that is to say a purely virtual particle. We work to the next-to-leading order of the expansion around the de Sitter background. The consistency of the approach puts a lower bound ($m_{\chi }>m_{\phi }/4$) on the mass $m_{\chi }$ of the fakeon with respect to the mass $m_{\phi }$ of the inflaton. The tensor-to-scalar ratio $r$ is predicted within less than an order of magnitude ($4/3 < N^{2}r<12$ to the leading order in the number of $e$-foldings $N$). Moreover, the relation $r\simeq -8n_{T}$ is not affected by the Weyl-squared term. No vector and no other scalar/tensor degree of freedom is present.
J. High Energy Phys. 07 (2020) 211 | DOI: 10.1007/JHEP07(2020)211
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. The fakeon does not have the problems of the Feynman-Wheeler propagator and emerges as the correct concept of purely virtual quantum. It allows us to make sense of quantum gravity at the fundamental level, and places it on an equal footing with the standard model. The resulting theory of quantum gravity is perturbative up to an incredibly high energy.
J. High Energ. Phys. 03 (2020) 142 | DOI: 10.1007/JHEP03(2020)142
Talk given at Penn State University, Dec 17, 2019
A new quantization prescription is able to endow quantum field theory with a new type of “particle”, the fakeon (fake particle), which mediates interactions, but cannot be observed. A massive fakeon of spin 2 (together with a scalar field) allows us to build a theory of quantum gravity that is both renormalizable and unitary, and to some extent unique. The theory predicts that causality is lost at sufficiently small distances, where time makes no longer sense. After presenting the general formulation of the theory, I explain its nontrivial classical limit, the modifications of the FLRW metric and the role of the cosmological constant. Finally, I discuss the possibility that the Higgs boson might be a fakeon.
The correspondence principle made of unitarity, locality and renormalizability has been very successful in quantum field theory. Among the other things, it helped us build the standard model. However, it also showed important limitations. For example, it failed to restrict the gauge group and the matter sector in a powerful way. After discussing its effectiveness, we upgrade it to make room for quantum gravity. The unitarity assumption is better understood, since it allows for the presence of physical particles as well as fake particles (fakeons). The locality assumption is applied to an interim classical action, since the true classical action is nonlocal and emerges from the quantization and a later process of classicization. The renormalizability assumption is refined to single out the special role of the gauge couplings. We show that the upgraded principle leads to an essentially unique theory of quantum gravity. In particular, in four dimensions, a fakeon of spin 2, together with a scalar field, is able to make the theory renormalizable while preserving unitarity. We offer an overview of quantum field theories of particles and fakeons in various dimensions, with and without gravity.
Proceedings of the conference “Progress and Visions in Quantum Theory in View of Gravity: Bridging foundations of physics and mathematics“, Max Planck Institute for Mathematics in the Sciences, Leipzig, October 2018
Talk given at the conference “Quantum Gravity and Quantum Geometry“, Nijmegen Oct 29 – Nov 1, 2019
A new quantization prescription is able to endow quantum field theory with a new type of “particle”, the fakeon (fake particle), which mediates interactions, but cannot be observed. A massive fakeon of spin 2 (together with a scalar field) allows us to build a theory of quantum gravity that is both renormalizable and unitary, and to some extent unique. The theory predicts that causality is lost at sufficiently small distances, where time makes no longer sense. After formulating the theory, I explain its main properties. In particular: the nontrivial classical limit, the modifications of the FLRW metric and the roles of the cosmological constant and the Hubble constant.
The concept of fake particle, or “fakeon”, allows us to make sense of quantum gravity as an ultraviolet complete theory, by renouncing causality at very small distances. We investigate whether the violation of microcausality can be amplified or detected in the most common settings. We show that it is actually short range for all practical purposes. Due to our experimental limitations, the violation does not propagate along the light cones or by means of gravitational waves. In some cases, the universe even conspires to make the effect disappear. For example, the positivity of the Hubble constant appears to be responsible for the direction of time in the early universe.
Class. Quantum Grav. 37 (2020) 095003 | DOI: 10.1088/1361-6382/ab78d2
We give a simple proof of perturbative unitarity in gauge theories and quantum gravity using a special gauge that allows us to separate the physical poles of the free propagators, which are quantized by means of the Feynman prescription, from the poles that belong to the gauge-trivial sector, which are quantized by means of the fakeon prescription. The proof applies to renormalizable theories, including the ultraviolet complete theory of quantum gravity with fakeons formulated recently, as well as low-energy (nonrenormalizable) theories. We clarify a number of subtleties related to the study of scattering processes in the presence of a cosmological constant $\Lambda$. The scattering amplitudes, defined by expanding the metric around flat space, obey the optical theorem up to corrections due to $\Lambda$, which are negligible for all practical purposes. Problems of interpretation would arise if such corrections became important. In passing, we obtain local, unitary (and “almost” renormalizable) theories of massive gravitons and gauge fields, which violate gauge invariance and general covariance explicitly.
J. High Energy Phys. 12 (2019) 027 | DOI: 10.1007/JHEP12(2019)027
Talk given by Marco Piva at the conference “Avenues of quantum field theory in curved spacetime“, Modena, Sept 9th, 2019
Talk given at the conference “Cosmological Frontiers in Fundamental Physics 2019” – Perimeter Institute
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Quantum Gravity 
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14B1 D. Anselmi
Renormalization
Course on renormalization, taught in 2015.
Last update: September 15th 2023, 242 pages
The final (2023) edition is vaibable on Amazon:
Contents:
Preface
1. Functional integral
2. Renormalization
3. Renormalization group
4. Gauge symmetry
5. Canonical formalism
6. Quantum electrodynamics
7. Non-Abelian gauge field theories
Notation and useful formulas
References
The pdf file of the 2015 Edition is available here: PDF
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