19S1 D. Anselmi
Theories of gravitation




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

Archive for June 2020

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, 2020


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 [hep-th])


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

arXiv: 2006.01163 [hep-th]


Search this site

YouTube Channel

Quantum Gravity Youtube Channel Quantum Gravity Quantum Gravity - Youtube Channel


14B1 D. Anselmi

Course on renormalization, taught in 2015.

Last update: September 15th 2023, 242 pages

The final (2023) edition is vaibable on Amazon:


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

The pdf file of the 2015 Edition is available here: PDF