Phd in Physics

Statistical field theory on the lattice

Statistical field theory on the lattice

Academic year 2024/2025

Sommario del corso

• Course objectives
• Results of learning outcomes
• Program
• Course delivery
• Learning assessment methods
• Suggested readings and bibliography
• Notes
• Class schedule
• Teaching tools
• Course card

Course objectives

This course contributes to the educational objectives of the Ph.D. in Physics and aims to provide a solid preparation in statistical field theory, with a specific focus on lattice field theory.

Results of learning outcomes

Knowledge and understanding

Acquisition of knowledge of statistical field theory, in particular for problems relevant to the description of strongly coupled quantum field theories in the lattice regularization.

Ability to apply knowledge and understanding

Acquisition of the ability to apply the knowledge of statistical field theory to solve problems relevant for non-perturbative phenomena in quantum field theory.

Autonomy of judgment

Acquisition of autonomy of conscious judgment, with reference to the evaluation and interpretation of theoretical problems related to the physics of strongly coupled quantum field theories, for the choice of suitable solution techniques for new situations.

Communication skills

Acquisition of skills and tools for communication in written and oral form, together with the use of the mathematical and formal language characteristic of analytical techniques to describe physical systems that can be studied in a statistical field theory approach.

Learning skills

Acquisition of autonomous learning skills and development of the skills to assess one's own preparation, aimed at undertaking subsequent further studies on the topics covered in the course with a high level of autonomy.

Program

Introduction and motivation

• Generalities about statistical field theory
• Lattice field theory
• Quantum chromodynamics on the lattice

Formalism

• Path integrals in quantum mechanics
• Path integrals in quantum field theory
• Scalar fields on the lattice

The lattice discretization for gauge theories

• Gauge fields on the lattice
• Improved actions and observables

Scale setting and phase structure of a lattice field theory

• Setting the scale
• Phase structure

Fermions on the lattice

• Naïve lattice discretization for fermions and the doubling problem
• Wilson fermions
• Staggered fermions
• Ginsparg-Wilson fermions

Numerical calculations in lattice field theory

• Motivation
• Brief introduction to Monte Carlo calculations
• Metropolis algorithm
• Algorithms for bosonic fields
• Algorithms for fermionic fields
• Extrapolations

Examples of numerical calculations in lattice QCD

• Spectroscopy
• Matrix elements
• The QCD running coupling

Lattice QCD at finite temperature and/or finite baryonic density

• Lattice QCD at finite temperature
• Lattice QCD at finite chemical potential

Some advanced topics

• Scattering amplitudes
• Heavy fermions on the lattice
• Effective theories for nuclear physics
• Spectral functions
• Renormalization on the lattice
• Some open problems

Course delivery

The course consists of 24 hours of lectures delivered in presence. Attendance is optional.

Communication with students is done via e-mail, after registration on the course webpage.

Learning assessment methods

The exam is a written test, in which the student is required to discuss some of the topics covered in the lessons.

Course notes in electronic format will be made available by the course lecturer.

Notes

Students with specific learning disorders (SLD) are invited to check the educational and/or technical aids (https://en.unito.it/services/students-special-needs/students-specific-learning-disorders-sld) and the access and welcome procedures (https://en.unito.it/services/students-special-needs/students-specific-learning-disorders-sld/entering-unito-students-sld) offered by the University of Turin, and in particular the support procedures for exams (https://en.unito.it/services/students-special-needs/students-specific-learning-disorders-sld/support-students-sld-taking).

Class schedule

• Teaching material
• Exams and finals
• Class schedule
• Go to Moodle
• Register for the course
• Enrolled students
• Invia email agli studenti registrati
• Export table