# 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

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

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

- Path Integral formulation of Quantum Mechanics, given by Prof. Griguolo;

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

- Black Hole Thermodynamics and Hawking radiation, given by Prof. Pietroni.

## Course contents

Part I:

- Path Integral formalism;

- Functional and Euclidean Methods;

- Semiclassical approximation.

Part II

- Entropy and Information;

- Maximal entropy variational principles and inference;

- Applications.

Part III

- Classical Black Holes;

- Metrics and Horizons;

- Pair creation and Hawking radiation;

- Black Hole Thermodynamics 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 bi 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.