ECTS - University of Pisa
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.
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.
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.
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.
Capacita` nel calcolare il valore delle osservabili fisiche nelle teorie di campo quantistiche
Computational expertise in determining the values of physical observables in quantum field theories.
Esercitazioni pratiche in classe
Exercise classes.
Students will acquire the ability to compute observable physical quantities from the first principles of a Quantum Field Theory
Students will acquire the ability to compute observable physical quantities from the first principles of a Quantum Field Theory
This will be checked during exercise classes and in the final exam
This will be checked during exercise classes and in the final exam
Quantum Mechanics, Special Relativity, Classical Mechanics
Quantum Mechanics, Special Relativity, Classical Mechanics
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Theoretical Physics II and other advanced courses dealing with various aspects of Quantum Field Theory
Theoretical Physics II and other advanced courses dealing with various aspects of Quantum Field Theory
Delivery: face to face lectures and exercise classes
Learning activities:
Attendance: Advised
Teaching methods:
Use of e-learning and Teams for course material or occasional online meetings.
Teachers available for clarifications (face-to-face, email or online meetings)
Delivery: face to face lectures and exercise classes
Learning activities:
Attendance: Advised
Teaching methods:
Use of e-learning and Teams for course material or occasional online meetings.
Teachers available for clarifications (face-to-face, email or online meetings)
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.
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.
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).
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).
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.
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.
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