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THEORETICAL PHYSICS 1
MASSIMO D'ELIA
Academic year2023/24
CoursePHYSICS
Code213BB
Credits9
PeriodSemester 1
LanguageItalian

ModulesAreaTypeHoursTeacher(s)
FISICA TEORICA 1FIS/02LEZIONI54
MASSIMO D'ELIA unimap
ALESSANDRO VICHI unimap
Obiettivi di apprendimento
Learning outcomes
Conoscenze

Il corso e` un'introduzione alle teorie di campo quantistiche, che sono usate per decrivere le interazioni fondamentali in fisica delle particelle e sistemi a molti corpi in materia condensata. In particolare, il corso si occupa della costruzione di teorie di campo relativisticamente invarianti, della costruzione di operatori di campo nello spazio di Fock, delle soluzioni dell'equazione di Dirac e di altre equazioni relativistiche, del calcolo delle ampiezze di transizione in teoria delle perturbazioni. 

Il corso e` pensato principalmente per fornire gli strumenti che permettono di ottenere informazioni quantitative per processi della fisica delle alte energie, come sezioni d'urto e rate di decadimento, all'ordine piu` basso nella teoria delle perturbazioni, usando la tecnica dei diagrammi di Feynamn e a partire da una generica teoria di campo effettiva. 

Knowledge

This course is an introduction to quantum field theories, which are generally used to describe fundamental interactions of particles and quantum many-body systems in condensed matter physics. In particular, the course deals with the construction of the field theory operators in Fock space, solutions of the Dirac equation,  computation of the transition amplitudes in perturbation theory. The course is supposed to provide the main tools to obtain quantitative information for high-energy processes, such as cross sections and decay rates of particles, at the leading order of perturbation theory using the technique of the Feynman diagrams, starting from given effective quantum field theories.

Modalità di verifica delle conoscenze

Gli studenti dovranno essere in grado di portare a termine il calcolo di osservabili fisiche a partire dai principi primi delle teorie quantistiche dei campi, e dovranno avere padronanza con i principi fondamentali alla base di quest'ultime.

Assessment criteria of knowledge

Students should be able to complete the computation of physical observables starting from the first principles of Quantum Field Theories, and should master the fundamental ideas at their basis.

 

Capacità

Capacita` nel calcolare il valore delle osservabili fisiche nelle teorie di campo quantistiche

Skills

Computational expertise in determining the values of physical observables in quantum field theories. 

Modalità di verifica delle capacità

Esercitazioni pratiche in classe

Assessment criteria of skills

Exercise classes.

 

Comportamenti

Students will acquire the ability to compute observable physical quantities from the first principles of a Quantum Field Theory

Behaviors

Students will acquire the ability to compute observable physical quantities from the first principles of a Quantum Field Theory

Modalità di verifica dei comportamenti

This will be checked during exercise classes and in the final exam

Assessment criteria of behaviors

This will be checked during exercise classes and in the final exam

Prerequisiti (conoscenze iniziali)

Quantum Mechanics, Special Relativity, Classical Mechanics 

Prerequisites

Quantum Mechanics, Special Relativity, Classical Mechanics 

Corequisiti

NA

Co-requisites

NA

Prerequisiti per studi successivi

Theoretical Physics II and other advanced courses dealing with various aspects of Quantum Field Theory

Prerequisites for further study

Theoretical Physics II and other advanced courses dealing with various aspects of Quantum Field Theory

 

Indicazioni metodologiche

Delivery: face to face lectures and exercise classes

Learning activities:

  • attending lectures
  • participation in discussions
  • individual study
  • group work

Attendance: Advised

Teaching methods:

  • Lectures and exercise classes.

Use of e-learning and Teams for course material or occasional online meetings.

Teachers available for clarifications (face-to-face, email or online meetings)

Teaching methods

Delivery: face to face lectures and exercise classes

Learning activities:

  • attending lectures
  • participation in discussions
  • individual study
  • group work

Attendance: Advised

Teaching methods:

  • Lectures and exercise classes.

Use of e-learning and Teams for course material or occasional online meetings.

Teachers available for clarifications (face-to-face, email or online meetings)

Programma (contenuti dell'insegnamento)

Concepts of classical field theory, hamiltonian and lagrangian formulation, symmetries and conserved quantities, Noether theorem.

Relativistic invariant field theories. Representations of the Poincare group. Relativistic wave equations for spin 0,1/2 and 1 particles. Unitary representations of the Poincare group on one particle states.

Second quantization, identical particles, Fock space. Locality, particles and antiparticles, connection between spin and statistics.

Field operators, wave functions, solutions of the Dirac equation, scalar fields,  massless and massive vector fields, spinor fields, covariant bilinears, Weyl spinors, discrete symmetries. 

Spinor electrodynamics, fields and lagrangian, gauge transformations and gauge invariance, minimal coupling.   

S matrix, computation of the transition amplitudes in perturbation theory, derivation of the decay widths and of the cross sections in particles processes. Feynman propagator, Wick theorem, Feynman diagrams. 

 

 

 

Syllabus

Concepts of classical field theory, hamiltonian and lagrangian formulation, symmetries and conserved quantities, Noether theorem.

Relativistic invariant field theories. Representations of the Poincare group. Relativistic wave equations for spin 0,1/2 and 1 particles. Unitary representations of the Poincare group on one particle states.

Second quantization, identical particles, Fock space. Locality, particles and antiparticles, connection between spin and statistics.

Field operators, wave functions, solutions of the Dirac equation, scalar fields,  massless and massive vector fields, spinor fields, covariant bilinears, Weyl spinors, discrete symmetries. 

Spinor electrodynamics, fields and lagrangian, gauge transformations and gauge invariance, minimal coupling.   

S matrix, computation of the transition amplitudes in perturbation theory, derivation of the decay widths and of the cross sections in particles processes. Feynman propagator, Wick theorem, Feynman diagrams. 

 

 

Bibliografia e materiale didattico
  • M. Maggiore, A Modern Introduction to Quantum Field Theory, Oxford University Press, (New York, 2005).
  • M.E. Peskin and D.V. Schroeder,  An Inntroduction to Quantum Field Theory, Westview Press (Boulder, 1995). 
  • F. Mandl and G. Shaw, Quantum Field Theory, John Wiley & Sons (New York, 1984).

  • C. Itzykson and J-B. Zuber, Quantum Field Theory, McGraw-Hill (Singapore, 1980).

Bibliography

 

  • M. Maggiore, A Modern Introduction to Quantum Field Theory, Oxford University Press, (New York, 2005).
  • M.E. Peskin and D.V. Schroeder,  An Inntroduction to Quantum Field Theory, Westview Press (Boulder, 1995). 
  • F. Mandl and G. Shaw, Quantum Field Theory, John Wiley & Sons (New York, 1984). 

  • C. Itzykson and J-B. Zuber, Quantum Field Theory, McGraw-Hill (Singapore, 1980).

Modalità d'esame

Esame finale sia scritto che orale. Nell'esame scritto gli studenti dovranno risolvere uno o piu` problemi articolati in varie domande e dimostrare la loro abilita` nel maneggiare le teorie quantistiche di campo che descrivono i processi fondamentali, ed i metodi computazionli per arrivare a calcolare le ampiezze di transizione. L'esame orale sara` di complemento a quello scritto, verificando le conoscenze generali sugli argomenti del corso.

Assessment methods

Both written and oral final examination. In the written exam students will solve one or more problems with various questions, demonstrate their ability in handling quantum field theories describing fundamental processes, and the methods to compute transition amplitudes. The oral exam will complement the written exam and test the general knowledge about the topics of the course.

 

Stage e tirocini

NA

Work placement

NA

Updated: 13/09/2023 00:30