# HIGHLIGHTS IN THORETICAL PHYSICS

## Learning outcomes of the course unit

After attending this course, the student is expected to be able to:

- Know the Path Integral formulation of Quantum Mechanics, and to apply it to the solution of problems, both through exact solutions, when existing, or by applying approximation methods;

- Know the relation between entropy and Information;

- Know and Apply statistical methods to simple interdisciplinary problems in data science;

- Know the basic properties of Black Holes, as well as the issues associated to their thermodynamical interpretation;

- Being able to find bibliographic references of frontline research topics and to evaluate the quality of scientific papers;

- Communicate effectively, through the preparation of scientific seminars on modern topics in theoretical physics.

- Being able to self-evaluate one's knowledge of a wide field such as modern theoretical physics, differentiating between conceptual and technical aspects.

## Prerequisites

Quantum Mechanics and basics in special Relativity

## Course contents summary

The lectures provide an overview on results and methods of modern Theoretical Physics.

This year, the course will be organised in two sections:

- Theormodynamical Entropy, Statistical Entropy and Information, with interdisciplinary applications to data science and learning given by Prof. Burioni;

- Path Integral formulation of Quantum Mechanics, Black Hole Thermodynamics and Hawking radiation, given by Prof. Pietroni.

## Course contents

First part:

- Thermodynamical Entropy and Statistical Entropy

- Irreversibility and the H theorem

- Relations between entropy and information;

- Variational principles of maximum entropy and statistical inference;

- Applications to Data science and learning.

Second part:

- Path Integral Path formalism;

- Functional and Euclidean methods;

- The semiclassical approximation.

- Classic Black Holes;

- Metrics and horizons;

- Creation of Couples and Hawking radiation;

- Thermodynamics of Black Holes and the "Information Paradox".

## Recommended readings

Lecture notes will be provided, to be integrated with other material suggested by the lecturers.

## Teaching methods

Blackboard lectures.

Notes of the lectures or of some of its parts, will be circulated via Elly.

## Assessment methods and criteria

oral examination. The student will prepare a short seminar on a subject agreed with the lecturers. This will be the initial part of the examination, which will go on with questions on the rest of the subjects taught during the course. The oral examination will last between 15 and 30 minutes. The evaluation will be agreed between the three lecturer, and will be communicated to the student immediately after the end of the interview.