Minicourse on perturbative and nonperturbative treatment of quantum gravity problems

May 20-24, 2024

ICTP-SAIFR, São Paulo, Brazil

IFT-UNESP Auditorium


The event is intended as a discussion of specific problems of quantum gravity, with the focus on non-traditional, i.e. qualitatively new, aspects and non-perturbative approaches. The general goal is to explain (or at least better understand) the main contradiction of quantum gravity, which is that the theory to be renormalizable always has higher derivatives, and therefore contains massive higher-derivative ghosts. This leads to classical and quantum instabilities and, in the quantum theory, the removal of ghosts from the spectrum violates the unitarity of the S-matrix. No known approaches to quantum gravity resolve the problem of ghosts in a satisfactory way, which we see as an indication that qualitatively new ideas need to be implemented.

Along with the planned discussions of the aforementioned issues, we will offer three introductory courses on quantum gravity. The mini-course of Prof. Asorey will review quantum gravity from a wide perspective, covering many different subjects. The mini-course by Prof. Menezes will provide an introduction to the basic notions and models of theories with higher derivatives. Finally, the mini-course of Prof. Shapiro will discuss the pertinent issue of decoupling theorems in gravity, which is relevant for determining in which theories of gravity we may expect a universal IR limit, i.e., quantum GR.

The necessary preliminary preparation of participants in this event includes standard courses of general relativity and quantum field theory.

There is no registration fee and limited funds are available for local expenses.

List of participants: Updated on May 22, 2024.

Survey: Here


Manuel Asorey (University of Zaragoza, Spain): Introduction to quantum gravity.

Gabriel Menezes (UFRRJ & IFT-UNESP): Higher Derivative Quantum Field Theories.

Ilya L. Shapiro (UFJF, MG): Some aspects of decoupling theorem and effective quantum gravity

Gastao Krein (IFT-UNESP): Complex-mass particles and their bound states.



Register: Monday 14:00 – 15:00 


1. Manuel Asorey (University of Zaragoza, Spain): Introduction to quantum gravity.

May 21, 22, 23. Time: 10:00 – 11:20

Lecture 1. Introduction to Quantum Gravity. Canonical formalism of Einstein gravity. DeWitt metric. Arnowit-Deser-Misner constraints analysis. Physical interpretation of constrains. Quantization. Wheeler-DeWitt equation. Wave function of the Universe. Minisuperspace. Conceptual issues.

Lecture 2. Covariant Formalism. Perturbation theory. Gauge fixing. Becchi Rouet Stora Tyutin symmetry and diffeomorphism invariance. One loop and two loop ultraviolet divergencies. Renormalization problems. Euclidean gravity. Gravitational instantons.

Lecture 3. Beyond Einstein’s theory. Higher derivative theories of Gravity. Singularities and black holes. Models of Inflation. Consistency checks. Kallen-Lehmann representation. Horava-Lifshitz theories. Infrared problems. Other approaches.

May 22. Time: 14:00

Colloquium: The New Gravitational Landscape


2. Gabriel Menezes (UFRRJ & IFT-UNESP): Higher Derivative Quantum Field Theories.

Reading Materials

May 20, 21. Time: 15:00 – 16:20

Lecture 1: General discussion; the Ostrogradsky problem; Pais-Uhlenbeck Oscillator: classical and quantum (canonical and path integral quantizations).

Lecture 2: Scalar field with higher-derivative term: Path-integral quantization, examples of scattering amplitudes, and discussion of unitarity, stability and causality.

May 22. Time: 15:30 – 16:50

Lecture 3: Applications — Lee-Wick O(n) model, Lee-Wick QED and Lee-Wick Standard Model, Quadratic Gravity.



3. Ilya L. Shapiro (UFJF, MG): Some aspects of decoupling theorem and effective quantum gravity

Date: May 23. Time: 15:00 – 16:20

Lecture 1. Basic calculations and basic results. One-loop Feynman diagrams and derivation of the nonlocal form factors for the two-point function. High-energy and low-energy limits. Quadratic decoupling in the IR. Curved-space calculation using the heat-kernel solution. Applications to the fourth-derivative terms in the one-loop effective action of gravity.

Date: May 24. Time  10:00 – 11:20

Lecture 2. Advanced subjects and complicated applications. Applications to the interacting theories. Appelquist and Carazzone theorem in QED. Decupling of massive degrees of freedom in polynomial higher derivative quantum gravity: mixed diagrams. Non-local theories of quantum gravity. On the possibility of the universal IR limit in quantum gravity.


4. Gastao Krein (IFT-UNESP): Complex-mass particles and their bound states.

Date: May 24. Time: 15:00





Application is now closed


Videos and Files

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Minicourse on perturbative and nonperturbative treatment of quantum gravity problems


Additional Information

Attention! Some participants in ICTP-SAIFR activities have received email from fake travel agencies asking for credit card information. All communication with participants will be made by ICTP-SAIFR staff using an e-mail “”. We will not send any mailings about accommodation that require a credit card number or any sort of deposit.

COVID-19: Brazilians and foreigners no longer have to present proof of vaccination before entering the country.

Visa information: Nationals from several countries in Latin America and Europe are exempt from tourist visa. Nationals from Australia, Canada and USA are exempt from tourist visa until April 10, 2024. Please check here which nationals need a tourist visa to enter Brazil.

Accommodation: Participants, whose accommodation will be provided by the institute, will stay at The Universe Flat. Hotel recommendations are available here.

How to reach the Institute: The program will be held at ICTP South American Institute, located at IFT-UNESP, which is across the street from a major bus and subway terminal (Terminal Barra Funda). The address which is closer to the entrance of the IFT-UNESP building is R. Jornalista Aloysio Biondi, 120 – Barra Funda, São Paulo. The easiest way to reach us is by subway or bus, please find instructions here.