ID:
500598
Duration (hours):
48
CFU:
6
SSD:
FISICA TEORICA, MODELLI E METODI MATEMATICI
Year:
2025
Overview
Date/time interval
Primo Semestre (22/09/2025 - 09/01/2026)
Syllabus
Course Objectives
The aim of the course is to provide students with the tools to deepen common properties of continuous media and with the basic concepts of classical field theory. After a general introduction to the mechanics of the continuum, the first part of the course is devoted to the acquisition of the basic knowledge of the dynamics of Newtonian fluids that possess inertia and viscosity. The second part of the course focuses on the relativistic classical field theory, taking classical electromagnetism as a prototype of a relativistic theory. After an introductory section that recalls the covariant formalism, a reformulation of the laws of electromagnetism is presented through the principle of minimum action. The importance of this principle, which constitutes in particular the starting point for the quantization of a classical system, derives from its general validity: it is applicable to any physical theory. In the final part of the course, of a more phenomenological nature, the most significant exact solutions of the electromagnetic equations are derived, describing the generation and propagation of waves, and the energy radiated in many physically relevant situations is analyzed.
Course Prerequisites
The course requires an adeguate knowledge of quantum physics as thaught in the course of modern physics and quantum mechanics of the bachelor degrees. The notions of classical electromagnetism and analytic mechanics are also assumed. Notions of special relativity are useful, although they will be briefly introduced before being applied.
Teaching Methods
The course is organised with classroom-taught lectures on the blackboard. During the lectures, the details necessary for the comprehension of the various theoretical topics are derived and explained. Homework assignments are complementary to the lectures and are focused to provide the tools for the application of the theoretical concepts and to improve the critical and personal comprehension. The assignments are discussed and corrected collectively.
Assessment Methods
The final exam consists in an oral test. The test is organised in two parts: 1- presentation of a topic
chosen by the student among the material discussed in the course, with a practical application to a physics case related to its program of study; 2- open-ended question focused to test the critical comprehension and analysis of the topics.
chosen by the student among the material discussed in the course, with a practical application to a physics case related to its program of study; 2- open-ended question focused to test the critical comprehension and analysis of the topics.
Texts
Lecturer's material made available and through the e-learning platform Kiro.
Other reference texts are:
1) A. J. Chorin and J. E. Marsden, "A Mathematical Introduction to Fluid Mechanics," (1992)
Springer
2) Mark S. Swanson, "Classical Field Theory and the Stress-Energy Tensor", (2015) Morgan & Claypool Publishers
3) K. Lechner, "Classical Electrodynamics: A Modern Perspective", (2018) Springer Nature
Other reference texts are:
1) A. J. Chorin and J. E. Marsden, "A Mathematical Introduction to Fluid Mechanics," (1992)
Springer
2) Mark S. Swanson, "Classical Field Theory and the Stress-Energy Tensor", (2015) Morgan & Claypool Publishers
3) K. Lechner, "Classical Electrodynamics: A Modern Perspective", (2018) Springer Nature
Contents
1) Continuous mechanics:
a) Continuous systems: Lagrangian and Eulerian description; material derivative and eulerian derivative; equation of continuity; transport theorem;
b) Principles and fundamental equations; Cauchy stress tensor; first and second cardinal equations; symmetry properties of the stress-tensor.
2) Newtonian fluid dynamics:
a) Perfect fluids: Euler equations and applications for a perfect fluid; Vorticity; Energy-momentum tensor for perfect fluids; Isentropic fluids; Incompressible fluids; Bernoulli's theorem and applications; Potential flows in 2d; Sound waves; The formulation with the principle of action of perfect fluids;
b) Viscous fluids and Navier-Stokes equations: Non-physicality of the dynamics of ideal fluids; Velocity gradient tensor; Stress tensor for Newtonian viscous fluids; Navier Stokes equations; Dimensional Navier Stokes equations and Reynolds number; Energy considerations and sign for the viscosity coefficient; Solution of Navier Stokes equations for unidirectional laminar flow between fixed parallel plates; Potential flow for irrotational, incompressible fluids; Blasius theorem; Kutta-Jukowski theorem; D'Alembert's paradox for non-viscous fluids in one dimension. Hydrodynamic Solitons.
3) Relativistic classical field theory:
a) Short summary of concepts from special relativity: Lorentz and Poincarè transformations; Infinitesimal transformations of the Poincarè group in relativistic field theory; Noether theorem for a general symmetry and in particular for the Poincaré group; Energy-momentum tensor and canonical angular momentum density.
b) The variation method in field theory: minimum action principle for a system of particles interacting with the electromagnetic field. The energy-momentum tensor of Electrodynamics.
c) Generation of electromagnetic fields: The Green function method; The general solution of Maxwell's equations; The fields of Lienard-Wiechert; Velocity fields and acceleration fields; The field of a charge in uniform motion.
Depending on the interests of the students, one of the following topics will be explored:
d) Relativistic radiation: relativistic formula of Larmor; Energy loss by radiation in high-energy circular and linear accelerators; Angular distribution of radiation in the ultrarelativistic limit.
e) Cerenkov effect: Main phenomenological aspects of the Cerenkov effect; Theoretical explanation; Radiation and formula of Frank and Tamm.
a) Continuous systems: Lagrangian and Eulerian description; material derivative and eulerian derivative; equation of continuity; transport theorem;
b) Principles and fundamental equations; Cauchy stress tensor; first and second cardinal equations; symmetry properties of the stress-tensor.
2) Newtonian fluid dynamics:
a) Perfect fluids: Euler equations and applications for a perfect fluid; Vorticity; Energy-momentum tensor for perfect fluids; Isentropic fluids; Incompressible fluids; Bernoulli's theorem and applications; Potential flows in 2d; Sound waves; The formulation with the principle of action of perfect fluids;
b) Viscous fluids and Navier-Stokes equations: Non-physicality of the dynamics of ideal fluids; Velocity gradient tensor; Stress tensor for Newtonian viscous fluids; Navier Stokes equations; Dimensional Navier Stokes equations and Reynolds number; Energy considerations and sign for the viscosity coefficient; Solution of Navier Stokes equations for unidirectional laminar flow between fixed parallel plates; Potential flow for irrotational, incompressible fluids; Blasius theorem; Kutta-Jukowski theorem; D'Alembert's paradox for non-viscous fluids in one dimension. Hydrodynamic Solitons.
3) Relativistic classical field theory:
a) Short summary of concepts from special relativity: Lorentz and Poincarè transformations; Infinitesimal transformations of the Poincarè group in relativistic field theory; Noether theorem for a general symmetry and in particular for the Poincaré group; Energy-momentum tensor and canonical angular momentum density.
b) The variation method in field theory: minimum action principle for a system of particles interacting with the electromagnetic field. The energy-momentum tensor of Electrodynamics.
c) Generation of electromagnetic fields: The Green function method; The general solution of Maxwell's equations; The fields of Lienard-Wiechert; Velocity fields and acceleration fields; The field of a charge in uniform motion.
Depending on the interests of the students, one of the following topics will be explored:
d) Relativistic radiation: relativistic formula of Larmor; Energy loss by radiation in high-energy circular and linear accelerators; Angular distribution of radiation in the ultrarelativistic limit.
e) Cerenkov effect: Main phenomenological aspects of the Cerenkov effect; Theoretical explanation; Radiation and formula of Frank and Tamm.
Course Language
Italian
More information
Students who fall under special categories (refer to portale.unipv.it/it/didattica/servizi-lo-studente/modalita-didattiche-inclusive for details) have access to course materials via KIRO. Upon request, they may also be granted permission to view recorded lectures from previous academic years through a dedicated link activated on KIRO. They are invited to contact the lecturer for online meetings and eventual group activities.
Degrees
Degrees (2)
PHYSICAL SCIENCES
Master’s Degree
2 years
SCIENZE FISICHE
Master’s Degree
2 years
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