Theory Lectures by Young Researchers - ThLYR 2022

4 Apr 2022, 09:00 → 31 Dec 2022, 18:00 Europe/Rome

Zoom Room (GGI)

Claudio Bonanno (INFN Firenze), William Giare' (GGI), Davide Maria Lombardo (GGI), Matteo Maria Maglio (Heidelberg U.), Yuan Miao (GGI), Imane Moumene (GGI), Shahram Vatani (GGI)

Th-LYR is a series of introductory web-lectures on specific research topics in Theoretical Physics, spanning Cosmology, Non-perturbative Approaches to Quantum Field Theories and Gauge Theories, String Theory, and Mathematical Physics. Lectures will be given by young researchers to young researchers in an informal and stimulating environment with extensive space for questions and discussions.

Monday 4 April

1 An Introduction to Quantum Computing for Lattice Quantum Field Theory - I

Classical state-of-the-art numerical techniques have pushed the measurements of quantities of interest for Lattice Quantum Field Theories to unprecedented degrees of accuracy.
However, these techniques have limitations and some problems are still difficult to investigate.
As Feynman noticed decades ago, quantum computation presents itself as a more natural setting to study the physics of quantum systems; as quantum computers and quantum technologies are improving from year to year, quantum computation techniques are becoming increasingly important tools in the theoretical physicist's toolkit.
In these lectures I will first give a broad introduction to the fundamentals of quantum computing,
discussing some of the main algorithms and applications.
Then, I will discuss some of the most promising quantum computing techniques for solving Lattice Quantum Field Theory problems in regimes where classical methods cannot be applied or are especially expensive from the computational point of view.

Speaker: Giuseppe Clemente (DESY Zeuthen)

Tuesday 5 April

2 An Introduction to Quantum Computing for Lattice Quantum Field Theory - II

Classical state-of-the-art numerical techniques have pushed the measurements of quantities of interest for Lattice Quantum Field Theories to unprecedented degrees of accuracy.
However, these techniques have limitations and some problems are still difficult to investigate.
As Feynman noticed decades ago, quantum computation presents itself as a more natural setting to study the physics of quantum systems; as quantum computers and quantum technologies are improving from year to year, quantum computation techniques are becoming increasingly important tools in the theoretical physicist's toolkit.
In these lectures I will first give a broad introduction to the fundamentals of quantum computing,
discussing some of the main algorithms and applications.
Then, I will discuss some of the most promising quantum computing techniques for solving Lattice Quantum Field Theory problems in regimes where classical methods cannot be applied or are especially expensive from the computational point of view.

Speaker: Giuseppe Clemente (DESY Zeuthen)

Tuesday 26 April

3 Techniques for statistical analysis of cosmological data - (Lecture 1 of 2)

Analyzing data is an interplay between modeling physical theories and using complex statistical inference to extract unbiased information from the data themselves. In the era of precision cosmology, data analysis has become a key tool for the falsification of cosmological theories and for the quest of finding new physical effects not predicted by our current modelization of the Universe.

Inevitably, many biases are introduced, willingly or not, in the procedure of extracting information from data since our theories are incomplete and our statistical inference is not perfect.  Such biases could lead to wrong physical conclusions and particular care is required in deriving answers that are as free as possible from those biases.

In this series of two lectures, I will give an introduction to Monte Carlo Markov Chain (MCMC) and Machine Learning (ML) techniques for the inference of cosmological parameters. I will discuss their advantages and disadvantages and show how they can be used to gain accurate information about our Universe.

The first lecture will be dedicated to introducing the building blocks of statistical inference. Starting from the simplest example of fitting a linear model to data, I will introduce the main  concepts behind the construction of MCMC and ML methods and show how to use them with real examples.

The second lecture will be dedicated to learning to use these methodologies to analyze real cosmological data and derive constraints on cosmological parameters. In particular, I will show the use of low-redshift (late-time) cosmological data to bound the Hubble parameter and discuss the results in view of the current literature on the Hubble tension.

Speaker: Fabrizio Renzi (Leiden University)

Wednesday 27 April

4 Techniques for statistical analysis of cosmological data - (Lecture 2 of 2)

Analyzing data is an interplay between modeling physical theories and using complex statistical inference to extract unbiased information from the data themselves. In the era of precision cosmology, data analysis has become a key tool for the falsification of cosmological theories and for the quest of finding new physical effects not predicted by our current modelization of the Universe.

Inevitably, many biases are introduced, willingly or not, in the procedure of extracting information from data since our theories are incomplete and our statistical inference is not perfect.  Such biases could lead to wrong physical conclusions and particular care is required in deriving answers that are as free as possible from those biases.

In this series of two lectures, I will give an introduction to Monte Carlo Markov Chain (MCMC) and Machine Learning (ML) techniques for the inference of cosmological parameters. I will discuss their advantages and disadvantages and show how they can be used to gain accurate information about our Universe.

The first lecture will be dedicated to introducing the building blocks of statistical inference. Starting from the simplest example of fitting a linear model to data, I will introduce the main  concepts behind the construction of MCMC and ML methods and show how to use them with real examples.

The second lecture will be dedicated to learning to use these methodologies to analyze real cosmological data and derive constraints on cosmological parameters. In particular, I will show the use of low-redshift (late-time) cosmological data to bound the Hubble parameter and discuss the results in view of the current literature on the Hubble tension.

Speaker: Fabrizio Renzi (Leiden University)

Thursday 5 May

5 An introduction to tensor models: from random geometry to melonic CFTs - (Lecture 1 of 2)

Tensor models are particularly interesting due to their melonic large-$N$ limit which is richer than the large-$N$ limit of vector models but simpler than the planar limit of matrix models. Tensor models were first introduced in zero dimension in the context of random geometry and quantum gravity. They were then extended to quantum mechanical models in one dimension as an alternative to the Sachdev-Ye-Kitaev model without disorder. Finally, they were generalized in higher dimensions as toy models for strongly-coupled QFTs. In this context, they give rise in the infrared to a new kind of conformal field theories analytically accessible, called melonic CFTs.

In these lectures, after reviewing the large-$N$ expansion of matrix models, I will introduce tensor models and derive their melonic large-$N$ limit. In both cases, I will present some applications to random geometry and quantum gravity. The second part of the lectures will focus on melonic CFTs. In particular, I will review the bosonic long-range $O(N)^3$ model giving rise at large $N$ to a unitary CFT in the infrared.

Speaker: Sabine Harribey (Ecole Polytechnique, CPHT and U. Heidelberg, ITP)

Friday 6 May

6 An introduction to tensor models: from random geometry to melonic CFTs - (Lecture 2 of 2)

Tensor models are particularly interesting due to their melonic large-$N$ limit which is richer than the large-$N$ limit of vector models but simpler than the planar limit of matrix models. Tensor models were first introduced in zero dimension in the context of random geometry and quantum gravity. They were then extended to quantum mechanical models in one dimension as an alternative to the Sachdev-Ye-Kitaev model without disorder. Finally, they were generalized in higher dimensions as toy models for strongly-coupled QFTs. In this context, they give rise in the infrared to a new kind of conformal field theories analytically accessible, called melonic CFTs.

In these lectures, after reviewing the large-$N$ expansion of matrix models, I will introduce tensor models and derive their melonic large-$N$ limit. In both cases, I will present some applications to random geometry and quantum gravity. The second part of the lectures will focus on melonic CFTs. In particular, I will review the bosonic long-range $O(N)^3$ model giving rise at large $N$ to a unitary CFT in the infrared.

Speaker: Sabine Harribey (Ecole Polytechnique, CPHT and U. Heidelberg, ITP)

Wednesday 11 May

7 Modern Non-Perturbative Techniques in QFT - Lecture 1

I will define quantum field theories (QFTs) Non-Perturbatively and discuss their observables. I will review modern techniques, such as the Conformal and S-matrix Bootstrap, which allow to bound the space of consistent QFTs and, in particular cases, even to compute some observables.

Speaker: Dr Karateev Denis (University of Geneva)

Thursday 12 May

8 Modern Non-Perturbative Techniques in QFT - Lecture 2

I will define quantum field theories (QFTs) Non-Perturbatively and discuss their observables. I will review modern techniques, such as the Conformal and S-matrix Bootstrap, which allow to bound the space of consistent QFTs and, in particular cases, even to compute some observables.

Speaker: Dr Karateev Denis (University of Geneva)

Tuesday 31 May

9 Density functionals in nuclear systems

In these two lectures, I will give a general overview of density functional theory (DFT) in nuclear systems. We will discuss the basic ingredients of the theory in terms of similarities and (of course) differences with an electronic system. We will discuss further, with an illustrating example, how to find the ground state properties of a simple nucleus and properties of infinite nuclear matter. We will end the discussion with constructing an energy density functional (EDF) which is cost effective, agnostic yet informed by nuclear properties, suitable for astrophysical calculations.

Speaker: Chiranjib Mondal (Université de Caen Normandie)

Friday 3 June

10 Density functionals in nuclear systems

In these two lectures, I will give a general overview of density functional theory (DFT) in nuclear systems. We will discuss the basic ingredients of the theory in terms of similarities and (of course) differences with an electronic system. We will discuss further, with an illustrating example, how to find the ground state properties of a simple nucleus and properties of infinite nuclear matter. We will end the discussion with constructing an energy density functional (EDF) which is cost effective, agnostic yet informed by nuclear properties, suitable for astrophysical calculations.

Speaker: Chiranjib Mondal (Université de Caen Normandie)

Wednesday 15 June

11 A Graph-Theoretic Approach to Free-Fermion Solvability

Abstract: The Jordan-Wigner transformation represents a profound connection between the physics of many-body spin systems and the physics of fermionic systems. In the setting where the effective fermions are noninteracting, the Jordan-Wigner transformation gives an exact solution method for an otherwise apparently complicated spin model.

I will describe a graph-theoretic framework which captures mappings to free fermions under a unified characterization, yielding new exact solutions to spin models. Remarkably, the relationships between exact-solution methods in this framework reflect the relationships between families of graphs. This suggests a promising approach to understanding the physics of many-body spin models through graph theory.

Speaker: Dr Adrian Chapman (Oxford)

Friday 17 June

12 A Graph-Theoretic Approach to Free-Fermion Solvability

Abstract: The Jordan-Wigner transformation represents a profound connection between the physics of many-body spin systems and the physics of fermionic systems. In the setting where the effective fermions are noninteracting, the Jordan-Wigner transformation gives an exact solution method for an otherwise apparently complicated spin model.

I will describe a graph-theoretic framework which captures mappings to free fermions under a unified characterization, yielding new exact solutions to spin models. Remarkably, the relationships between exact-solution methods in this framework reflect the relationships between families of graphs. This suggests a promising approach to understanding the physics of many-body spin models through graph theory.

Speaker: Adrian Chapman (Oxford)

Tuesday 28 June

13 The frontier of feebly interacting particles: from dark matter to the muon (g-2)

New light but Feebly Interacting Particles (FIPs) represent an
exciting and well-motivated class of new physics particles.
FIPs are loosely defined as (1) singlets under the Standard
Model (SM) gauge groups; (2) lighter than the electroweak
scale and (3) not yet excluded or discovered.
Many well-grounded new physics candidates fit this
definition, with extremely bright experimental prospects for
FIPs in the MeV and GeV mass range.
In these lectures, we will present the theoretical foundations
of this family of new physics particles and introduce some of
its most searched-for members. The links between FIPs and
the dark matter problem will be explored, along with their
potential in explaining various low-energy experimental
anomalies, including the measured anomalous magnetic
moment.

Speaker: Luc Darmé (IP2I)

Friday 1 July

14 The frontier of feebly interacting particles: from dark matter to the muon (g-2)

New light but Feebly Interacting Particles (FIPs) represent an
exciting and well-motivated class of new physics particles.
FIPs are loosely defined as (1) singlets under the Standard
Model (SM) gauge groups; (2) lighter than the electroweak
scale and (3) not yet excluded or discovered.
Many well-grounded new physics candidates fit this
definition, with extremely bright experimental prospects for
FIPs in the MeV and GeV mass range.
In these lectures, we will present the theoretical foundations
of this family of new physics particles and introduce some of
its most searched-for members. The links between FIPs and
the dark matter problem will be explored, along with their
potential in explaining various low-energy experimental
anomalies, including the measured anomalous magnetic
moment.

Speaker: Luc Darmé (IP2I)