### Course

19S1 D. Anselmi
Theories of gravitation

Program

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### Book

D. Anselmi
From Physics To Life

A journey to the infinitesimally small and back

In English and Italian

Available on Amazon:
US: book | ebook  (in EN)
IT: book | ebook  (in IT)

## Unitarity

We prove spectral optical identities in quantum field theories of physical particles (defined by the Feynman $i\epsilon$ prescription) and purely virtual particles (defined by the fakeon prescription). The identities are derived by means of purely algebraic operations and hold for every (multi)threshold separately and for arbitrary frequencies. Their major significance is that they offer a deeper understanding on the problem of unitarity in quantum field theory. In particular, they apply to “skeleton” diagrams, before integrating on the space components of the loop momenta and the phase spaces. In turn, the skeleton diagrams obey a spectral optical theorem, which gives the usual optical theorem for amplitudes, once the integrals on the space components of the loop momenta and the phase spaces are resumed. The fakeon
prescription/projection is implemented by dropping the thresholds that involve fakeon frequencies. We give examples at one loop (bubble, triangle, box, pentagon and hexagon), two loops (triangle with “diagonal”, box with diagonal) and arbitrarily many loops. We also derive formulas for the loop integrals with fakeons and relate them to the known formulas for the loop integrals with physical particles.

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arXiv: 2109.06889 [hep-th]

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.

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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.

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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.

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J. High Energy Phys. 12 (2019) 027 | DOI: 10.1007/JHEP12(2019)027

arXiv: 1909.04955 [hep-th]

Talk given by Marco Piva at the conference “Avenues of quantum field theory in curved spacetime“, Modena, Sept 9th, 2019

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Talk given at the conference “Gravity and other fields under the volcano”, Catania, Italy, June 10th, 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. After presenting the general properties of this theory, I discuss its classical limit, which carries important remnants of the fakeon quantization prescription. I also discuss the possibility that the Higgs boson might be a fakeon.

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We point out the idea that, at small scales, gravity can be described by the standard degrees of freedom of general relativity, plus a scalar particle and a degree of freedom of a new type: the fakeon. This possibility leads to fundamental implications in understanding gravitational force at quantum level as well as phenomenological consequences in the corresponding classical theory.

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Int. J. Mod. Phys. D 28 (2019) 1944007 | DOI: 10.1142/S0218271819440073

arXiv: 1905.06516 [hep-th]

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. After presenting the general properties of this theory, I discuss its classical limit, which carries important remnants of the fakeon quantization prescription and reveals unforeseen features.

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Under certain assumptions, it is possible to make sense of higher derivative theories by quantizing the unwanted degrees of freedom as fakeons, which are later projected away. Then the true classical limit is obtained by classicizing the quantum theory. Since quantum field theory is formulated perturbatively, the classicization is also perturbative. After deriving a number of properties in a general setting, we consider the theory of quantum gravity that emerges from the fakeon idea and study its classicization, focusing on the FLRW metric. We point out cases where the fakeon projection can be handled exactly, which include radiation, the vacuum energy density and the combination of the two, and cases where it cannot, which include dust. Generically, the classical limit shares many features with the quantum theory it comes from, including the impossibility to write down complete, “exact” field equations, to the extent that asymptotic series and nonperturbative effects come into play.

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J. High Energy Phys. 04 (2019) 61 | DOI: 10.1007/JHEP04(2019)061

arXiv: 1901.09273 [gr-qc]

Hal-02368987

Talk given at the Department of Physics and Astronomy of Southampton University, UK, on Nov 16th, 2018

I introduce the concept of fake particle and study how it is used to formulate a consistent theory of quantum gravity. Fakeons arise from a new quantization prescription, alternative to the Feynman one, for the poles of higher-derivative theories, which avoids the problem of ghosts. The fake particles mediate interactions and simulate true particles in many situations. Nevertheless, they are not asymptotic states and cannot be detected directly. The Wick rotation and the S matrix are regionwise analytic and the amplitudes can be calculated in all regions starting from the Euclidean one by means of an unambiguous, but nonanalytic operation. By reconciling renormalizability and unitarity in higher-derivative theories, the models containing both true and fake particles are good candidates to explain quantum gravity. In pole position is the unique theory that is strictly renormalizable. One of the major physical predictions due to the fakeons is the violation of microcausality. I discuss the classical limit of the theory and the acausal corrections to the Einstein equations.

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Quantum Gravity

### Book

14B1 D. Anselmi
Renormalization

Course on renormalization, taught in Pisa in 2015. (More chapters will be added later.)

Last update: May 9th 2015, 230 pages

Avaibable 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

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