### Course

19S1 D. Anselmi
Theories of gravitation

Program

PDF

### 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)

### Recent papers and theorems

21A5 Damiano Anselmi
Diagrammar of physical and fake particles and spectral optical theorem

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 ... [more]

21A4 Damiano Anselmi, Kristjan Kannike, Carlo Marzo, Luca Marzola, Aurora Melis, Kristjan Müürsepp, Marco Piva and Martti Raidal
A fake doublet solution to the muon anomalous magnetic moment

Extensions to the Standard Model that use strictly off-shell degrees of freedom - the fakeons - allow for new measurable interactions at energy scales usually precluded by the constraints that target the on-shell propagation of new particles. Here we employ the interactions between a new fake scalar doublet and the ... [more]

21A3 Damiano Anselmi, Kristjan Kannike, Carlo Marzo, Luca Marzola, Aurora Melis, Kristjan Müürsepp, Marco Piva, Martti Raidal
Phenomenology of a Fake Inert Doublet Model

We introduce a new way of modeling the physics beyond the Standard Model by considering fake, strictly off-shell degrees of freedom: the fakeons. To demonstrate the approach and exemplify its reach, we re-analyze the phenomenology of the Inert Doublet Model under the assumption that the second doublet is a fakeon. ... [more]

21A2 Damiano Anselmi
Perturbation spectra and renormalization-group techniques in double-field inflation and quantum gravity cosmology

We study primordial cosmology with two scalar fields that participate in inflation at the same time, by coupling quantum gravity (i.e., the theory $R+R^2+C^2$ with the fakeon prescription/projection for $C^2$) to a scalar field with a quadratic potential. We show that there exists a perturbative regime that can be described by ... [more]

21A1 Damiano Anselmi, Filippo Fruzza and Marco Piva
Renormalization-group techniques for single-field inflation in primordial cosmology and quantum gravity

We study inflation as a "cosmic" renormalization-group flow. The flow, which encodes the dependence on the background metric, is described by a running coupling $\alpha$, which parametrizes the slow roll, a de Sitter free, analytic beta function and perturbation spectra that are RG invariant in the superhorizon limit. Using ... [more]

20S5 Damiano Anselmi
Primordial cosmology from quantum gravity with purely virtual particles

Online talk for the Kavli Institute for Cosmology, Institute of Astronomy, University of Cambridge Abstract: I introduce the concept of purely virtual particle, or fakeon, and show how to use to make sense of quantum gravity as a quantum field theory. Then I discuss novel features of the classical limit and ... [more]

20S4 Damiano Anselmi
Quantum gravity with purely virtual particles: from quantum field theory to primordial cosmology

Online talk for the Max-Planck-Institut für Kernphysik, (MPIK), Heidelberg, Germany Abstract: I introduce the concept of purely virtual particle, or fakeon, and show how to use to make sense of quantum gravity as a quantum field theory. Then I discuss novel features of the classical limit and derive predictions in inflationary cosmology ... [more]

20S3 Damiano Anselmi
Quantum gravity with purely virtual particles: from quantum field theory to primordial cosmology

Talk at NICPB, Tallinn, Estonia, Oct 14th, 2020 Abstract: I introduce the concept of purely virtual particle, or fakeon, and show how to use to make sense of quantum gravity as a quantum field theory. Then I discuss novel features of the classical limit and derive predictions in inflationary cosmology that ... [more]

20A5 Damiano Anselmi
High-order corrections to inflationary perturbation spectra in quantum gravity

We compute the inflationary perturbation spectra and the quantity $r+8n_{T}$ to the next-to-next-to-leading log order in quantum gravity with purely virtual particles (which means the theory $R+R^{2}+C^{2}$ with the fakeon prescription/projection for $C^{2}$). The spectra are functions of the inflationary running coupling $\alpha (1/k)$ and satisfy the cosmic renormalization-group flow ... [more]

20A4 Damiano Anselmi
Cosmic inflation as a renormalization-group flow: the running of power spectra in quantum gravity

We study the running of power spectra in inflationary cosmology as a renormalization-group flow from the de Sitter fixed point. The beta function is provided by the equations of the background metric. The spectra of the scalar and tensor fluctuations obey RG evolution equations with vanishing anomalous dimensions in the ... [more]

20S2 Marco Piva
Predictions in inflationary cosmology from quantum gravity with purely virtual quanta

Testable predictions of quantum gravity with fakeons on the spectra of the CMB radiation Based on the paper 20A3 Renorm (arXiv: 2006.01163 [hep-th]) Talk given online by M. Piva for the Tokyo Institute of Technology, on Jun 16th, 2020 Talk given online by Marco Piva for the University of Sussex, on July 20th, ... [more]

20S1 Marco Piva
Predictions in inflationary cosmology from quantum gravity with purely virtual quanta

Testable predictions of quantum gravity with fakeons on the spectra of the CMB radiation Talk given by M. Piva at the National Institute of Chemical Physics and Biophysics, Tallinn, Estonia, on Jun 9th, 2020 Based on the paper 20A3 Renorm (arXiv: 2006.01163 ... [more]

20A3 Damiano Anselmi
Quantum field theories of arbitrary-spin massive multiplets and Palatini 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 ... [more]

20A2 Damiano Anselmi, Eugenio Bianchi and Marco Piva
Predictions of quantum gravity in inflationary cosmology: effects of the Weyl-squared term

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. ... [more]

20A1 Damiano Anselmi
The quest for purely virtual quanta: fakeons versus Feynman-Wheeler particles

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 ... [more]

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.

PDF

arXiv: 2109.06889 [hep-th]

Extensions to the Standard Model that use strictly off-shell degrees of freedom – the fakeons – allow for new measurable interactions at energy scales usually precluded by the constraints that target the on-shell propagation of new particles. Here we employ the interactions between a new fake scalar doublet and the muon to explain the recent Fermilab measurement of its anomalous magnetic moment. Remarkably, unlike in the case of usual particles, the experimental result can be matched for fakeon masses below the electroweak scale without contradicting the stringent precision data and collider bounds on new light degrees of freedom. Our analysis, therefore, demonstrates that the fakeon approach offers unexpected viable possibilities to model new physics naturally at low scales.

PDF

Phys. Rev. D 104 (2021) 035009 | DOI: 10.1103/PhysRevD.104.035009

arXiv: 2104.03249 [hep-ph]

We introduce a new way of modeling the physics beyond the Standard Model by considering fake, strictly off-shell degrees of freedom: the fakeons. To demonstrate the approach and exemplify its reach, we re-analyze the phenomenology of the Inert Doublet Model under the assumption that the second doublet is a fakeon. Remarkably, the fake doublet avoids the most stringent $Z$-pole constraints regardless of the chosen mass scale, thereby allowing for the presence of new effects well below the electroweak scale. Furthermore, the absence of on-shell propagation prevents fakeons from inducing missing energy signatures in collider experiments. The distinguishing features of the model appear at the loop level, where fakeons modify the Higgs boson $h\rightarrow\gamma\gamma$ decay width and the Higgs trilinear coupling. The running of Standard Model parameters proceeds as in the usual Inert Doublet Model case. Therefore, the fake doublet can also ensure the stability of the Standard Model vacuum. Our work shows that fakeons are a valid alternative to the usual tools of particle physics model building, with the potential to shape a new paradigm, where the significance of the existing experimental constraints towards new physics must necessarily be reconsidered.

PDF

to appear in J. High Energy Phys.

arXiv: 2104.02071 [hep-ph]

We study primordial cosmology with two scalar fields that participate in inflation at the same time, by coupling quantum gravity (i.e., the theory $R+R^2+C^2$ with the fakeon prescription/projection for $C^2$) to a scalar field with a quadratic potential. We show that there exists a perturbative regime that can be described by an asymptotically de Sitter, cosmic RG flow in two couplings. Since the two scalar degrees of freedom mix in nontrivial ways, the adiabatic and isocurvature perturbations are not RG invariant on superhorizon scales. It is possible to identify the correct perturbations by using RG invariance as a guiding principle. We work out the resulting power spectra of the tensor and scalar perturbations to the NNLL and NLL orders, respectively. An unexpected consequence of RG invariance is that the theory remains predictive. Indeed, the scalar mixing affects only the subleading corrections, so the predictions of quantum gravity with single-field inflation are confirmed to the leading order.

PDF

J. Cosmol. Astropart. Phys. 07 (2021) 037 | DOI: 10.1088/1475-7516/2021/07/037

arXiv: 2105.05864 [hep-th]

We study inflation as a “cosmic” renormalization-group flow. The flow, which encodes the dependence on the background metric, is described by a running coupling $\alpha$, which parametrizes the slow roll, a de Sitter free, analytic beta function and perturbation spectra that are RG invariant in the superhorizon limit. Using RG invariance as a guiding principle, we classify the main types of flows according to the properties of their spectra, without referring to their origins from specific actions or models. Novel features include spectra with essential singularities in $\alpha$ and violations of the relation $r+8n_{\text{t}}=0$ to the leading order. Various classes of potentials studied in the literature can be described by means of the RG approach, even when the action includes a Weyl-squared term, while others are left out. In known cases, the classification helps identify the models that are ruled out by data. The RG approach is also able to generate spectra that cannot be derived from standard Lagrangian formulations.

PDF

arXiv: 2103.01653 [hep-th]

The Youtube Channel Quantum Gravity has just crossed the threshold of 1100 subscribers. Its URL address is http://youtube.com/c/QuantumGravityTheory.

Quick statistics up to date, at 3 years since creation:

Total number of views: 68.6 k
Total watched time: 10.6 k hours
Number of subscribers: 1103
Number of videos: 130

Most watched videos:

I quanti e la quasi realtà: 3090 views, 756 hours, 82 likes
Quantum gravity from fakeons – Catania 2019: 2910 views, 87.5 hours, 32 likes
Quantum gravity al pub: 2767 views, 651 hours, 45 likes
L’atomo: 2514 views, 238 hours, 106 likes

Theories of Gravitation Lecture 1: 2033 views, 100 hours, 27 likes
La MQ mette a dura prova la ns comprens. della natura: 1835 views, 571 hours, 51 likes
Entanglement. Tagliare l’atomo come il burro: 1533 views, 221 hours, 61 likes
Il principio di indeterminazione: 1485 views, 246 hours, 67 likes
La gravità quantistica: 1482 views, 280 hours, 60 likes

La fisica e la vita – Viaggio nell’infinitamente piccolo, e ritorno: 1417 views, 165 hours, 19 likes

Number of visits to this website since creation (2013): 51.4 k

17A3 On the quantum field theory of the grav. interactions: 1033 downloads (2 archives)
18A7 On The Nature of the Higgs Boson: 427 downloads (4 archives)

Last update: Sept 16, 2021

Online talk for the Kavli Institute for Cosmology, Institute of Astronomy, University of Cambridge

Abstract: I introduce the concept of purely virtual particle, or fakeon, and show how to use to make sense of quantum gravity as a quantum field theory. Then I discuss novel features of the classical limit and derive predictions in inflationary cosmology that could be tested in the forthcoming years, paying special attention to the effects of fakeons on perturbation spectra

PDF

Online talk for the Max-Planck-Institut für Kernphysik, (MPIK), Heidelberg, Germany

Abstract: I introduce the concept of purely virtual particle, or fakeon, and show how to use to make sense of quantum gravity as a quantum field theory. Then I discuss novel features of the classical limit and derive predictions in inflationary cosmology that could be tested in the forthcoming years, paying special attention to the effects of fakeons on perturbation spectra

PDF

Talk at NICPB, Tallinn, Estonia, Oct 14th, 2020

Abstract: I introduce the concept of purely virtual particle, or fakeon, and show how to use to make sense of quantum gravity as a quantum field theory. Then I discuss novel features of the classical limit and derive predictions in inflationary cosmology that could be tested in the forthcoming years, paying special attention to the effects of fakeons on perturbation spectra

PDF

We compute the inflationary perturbation spectra and the quantity $r+8n_{T}$ to the next-to-next-to-leading log order in quantum gravity with purely virtual particles (which means the theory $R+R^{2}+C^{2}$ with the fakeon prescription/projection for $C^{2}$). The spectra are functions of the inflationary running coupling $\alpha (1/k)$ and satisfy the cosmic renormalization-group flow equations, which determine the tilts and the running coefficients. The tensor fluctuations receive contributions from the spin-2 fakeon $\chi _{\mu \nu }$ at every order of the expansion in powers of $\alpha \sim 1/115$. The dependence of the scalar spectrum on the $\chi _{\mu \nu }$ mass $m_{\chi }$, on the other hand, starts from the $\alpha^{2}$ corrections, which are handled perturbatively in the ratio $m_{\phi}/m_{\chi }$, where $m_{\phi }$ is the inflaton mass. The predictions have theoretical errors ranging from $\alpha ^{4}\sim 10^{-8}$ to $\alpha^{3}\sim 10^{-6}$. Nontrivial issues concerning the fakeon projection at higher orders are addressed.

PDF

J. Cosmol. Astropart. Phys. 02 (2021) 029 | DOI: 10.1088/1475-7516/2021/02/029

arXiv: 2010.04739 [hep-th]

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

PDF