Unit THEORETICAL PHYSICS
- Course
- Physics
- Study-unit Code
- GP005476
- Location
- PERUGIA
- Curriculum
- In all curricula
- CFU
- 16
- Course Regulation
- Coorte 2017
- Offered
- 2017/18
- Type of study-unit
- Obbligatorio (Required)
- Type of learning activities
- Attività formativa integrata
THEORETICAL PHYSICS PART 1
| Code | GP005492 |
|---|---|
| Location | PERUGIA |
| CFU | 6 |
| Teacher | Maria Cristina Diamantini |
| Teachers |
|
| Hours |
|
| Learning activities | Caratterizzante |
| Area | Teorico e dei fondamenti della fisica |
| Academic discipline | FIS/02 |
| Type of study-unit | Obbligatorio (Required) |
| Language of instruction | Italian |
| Contents | Discrete symmetries, parity and time reversal. Introduction to groups theory. Lie groups and Lie algebras. Lorentz and Poincare groups. Representations: scalars, spinors and vectors. Introduction to relativistic quantum mechanics; Klein-Gordon and Dirac equation. Lagrangian field theory. Second quantization of free fields. |
| Reference texts | Itzykson-Zuber, Quantum Field Theory Ramond, Field Theory Georgi: Lie Algebras in Particle Physics Mandl-Shaw, Field Theory |
| Educational objectives | Aim of the course is the introduction to relativistic quantum mechanics and the introduction to free field theory. |
| Prerequisites | Knowledge of non-relativistic quantum mechanics and special relativity are required. |
| Teaching methods | Theory courses |
| Other information | None |
| Learning verification modality | The first part of the course (Module I) does not have a separate final exam. However, written tests will be submitted to the students during the semester. |
| Extended program | Discrete symmetries in quantum mechanics. Parity. Anti-unitary operators, time-reversal. Introduction to groups theory. Lie groups and Lie algebras. Example of rotations group SO(3). Lorentz and Poincare groups. Representations: scalars, spinors and vectors. Introduction to relativistic quantum mechanics; Klein-Gordon and Dirac equation. Lagrangian field theory. Second quantization of free fields. |
THEORETICAL PHYSICS PART 2
| Code | GP005493 |
|---|---|
| Location | PERUGIA |
| CFU | 10 |
| Teacher | Andrea Marini |
| Teachers |
|
| Hours |
|
| Learning activities | Caratterizzante |
| Area | Teorico e dei fondamenti della fisica |
| Academic discipline | FIS/02 |
| Type of study-unit | Obbligatorio (Required) |
| Language of instruction | Italian |
| Contents | • Elements of group theory and representation theory; • Lorentz and Poincaré groups;¿ • Introduction to quantum field theory;¿ • Quantization of free fields (scalar, Dirac and gauge fields); • Interacting fields; • Quantum electrodynamics (QED); • Hint of radiative corrections and renormalization. |
| Reference texts | For the Group Theory part:¿ • W.-K. Tung, Group Theory in Physics¿ • G. Fonda, G. Ghirardi, Symmetry Principles in Quantum Physics • H. Georgi, Lie Algebras in Particle Physics For the Quantum Field Theory part:¿ • F. Mandl, G. Shaw, Quantum Field Theory ¿ • M. Peskin, D. Schroeder, An Introduction to Quantum Field Theory • L.H. Ryder, Quantum Field Theory • C. Itzykson, J.-B. Zuber, Quantum Field Theory¿ • J. Bjorken, S. Drell, Relativistic Quantum Fields |
| Educational objectives | The course aims to provide the students with the main notions of the quantum field theory formalism. The students should gain knowledge of the perturbative approach to study interacting field theories and of the diagrammatic picture given by Feynman diagrams. Using this approach they should be able to compute (tree-level) amplitudes of quantum electrodynamics processes. |
| Prerequisites | In order to be able to understand the arguments treated in the course an in-depth knowledge of Quantum mechanics and Special Relativity is needed. |
| Teaching methods | The course is organized as follows: • Lectures on all the subjects of the course; • Assignments of problem sets to be made in preparation of the exam. |
| Other information | None. |
| Learning verification modality | The exam consists in an oral interview, about one hour long, aiming to assess the knowledge level and the understanding capabilities achieved by the student on the theoretical and methodological contents as indicated on the course program. |
| Extended program | Elements of group theory Structure of groups; subgroups, classes and invariant subgroups; cosets and factor groups; homomorphisms and isomorphisms; direct product. Group representations; equivalent representations; unitary representations; reducible and irreducible representations. Topological groups and Lie groups; compactness; connected groups; universal covering; generators; Lie algebra; Casimir operators. Relevant exampls: SU(2); SO(3) and its universal covering. Lorentz and Poincaré groups Lorentz group: definition and classification of Lorentz transformations; restricted Lorentz group and its universal covering; spinorial representation; Lorentz algebra; Casimir; relevant representations: scalars, vectors, Weyl and Dirac spinors. Poincaré group: algebra and Casimir; unitary representations. Introduction to quantum field theory Relativistic quantum mechanics; Klein-Gordon equation; problems in the single particle interpretation; Dirac equation; particles e anti-particles. motivation to quantum field theory. Classical field theory: Lagrangian formulation; Lorentz invariance and locality. Noether theorem. Quantization of free fields Real scalar field: Klein-Gordon equation and action principle; expansion in normal modes. Quantization of the free real scalar field; creation and annihilation operators; normal product; Fock space. Complex scalar field. Scalar Feynman propagator. Spinorial Dirac field: action principle; Noether currents; discrete symmetries (CPT). Fierz transformations. Plane-wave solution of the free Dirac equation; anti-commutation rules; Fock space and Fermi-Dirac statistic. Fermionic Feynman propagator. Electromagnetic field: Maxwell equations and action principle; gauge symmetry. Covariant quantization of the e.m. field; Gupta-Bleuler condition; Fock space. Photon Feynman propagator. Interacting fields: Quantum electrodynamics (QED) Spinor quantum electrodynamics: minimal coupling and gauge. Interaction picture; S matrix. Wick theorem. Feynman diagrams. Feynman rules for QED. Elementary processes: electron-positron annihilation and creation of muon-antimuon; electron scattering; electron-positron annihilation; Bhabha scattering; Compton scattering. Hint of radiative corrections and renormalization Källén-Lehmann spectral representation. Mass and charge renormalization in QED. |