Fisica | ELECTRODYNAMICS AND GRAVITATION

cod. 0522600004

ELECTRODYNAMICS AND GRAVITATION

	0522600004
	DIPARTIMENTO DI FISICA "E.R. CAIANIELLO"
	EQF7
	PHYSICS
	2016/2017

PERCORSO COMUNE

	OBBLIGATORIO
	YEAR OF COURSE 1
	YEAR OF DIDACTIC SYSTEM 2014
	PRIMO SEMESTRE

TEACHING UNITS

	SSD	CFU	HOURS	ACTIVITY	TYPE OF ACTIVITY
	FIS/02	6	48	LESSONS	COMPULSORY SUBJECTS, CHARACTERISTIC OF THE CLASS

PROFESSORS

	GAETANO LAMBIASE T Curriculum
	ANTONIO CAPOLUPO Curriculum

	Objectives
	KNOWLEDGE AND UNDERSTANDING: THE COURSE AIMS TO INTRODUCE STUDENTS TO THE FUNDAMENTALS OF ELECTRODYNAMICS (ELECTROMAGNETISM IN ITS FULLY RELATIVISTIC FORMULATION) AND TO THE FIRST ELEMENTS OF RELATIVISTIC GRAVITATION, EMPHASIZING DIFFERENCES, SIMILARITIES AND APPLICATIONS. APPLYING KNOWLEDGE AND UNDERSTANDING: THE AIM IS TO MAKE STUDENTS ABLE TO HANDLE THEORETICAL NOTIONS AND APPLICATIONS IN THE FIELDS LISTED ABOVE. THIS SHOULD FAVOUR THE POSSIBILITY OF INCLUSION IN NATIONAL AND INTERNATIONAL RESEARCH INSTITUTIONS, AS WELL AS IN DIFFERENT WORKING ENVIRONMENTS.

KNOWLEDGE AND UNDERSTANDING:
THE COURSE AIMS TO INTRODUCE STUDENTS TO THE FUNDAMENTALS OF ELECTRODYNAMICS (ELECTROMAGNETISM IN ITS FULLY RELATIVISTIC FORMULATION) AND TO THE FIRST ELEMENTS OF RELATIVISTIC GRAVITATION, EMPHASIZING DIFFERENCES, SIMILARITIES AND APPLICATIONS.

APPLYING KNOWLEDGE AND UNDERSTANDING:
THE AIM IS TO MAKE STUDENTS ABLE TO HANDLE THEORETICAL NOTIONS AND APPLICATIONS IN THE FIELDS LISTED ABOVE. THIS SHOULD FAVOUR THE POSSIBILITY OF INCLUSION IN NATIONAL AND INTERNATIONAL RESEARCH INSTITUTIONS, AS WELL AS IN DIFFERENT WORKING ENVIRONMENTS.

	Prerequisites
	MATHEMATICAL ANALYSIS, GEOMETRY, GENERAL PHYSICS, LAGRANGIAN AND HAMILTONIAN DYNAMICS, SPECIAL RELATIVITY, QUANTUM MECHANICS.

	Contents
	1) ELECTRODYNAMICS: SPECIAL RELATIVITY. LORENTZ TRANSFORMATIONS. GENERATORS OF BOOSTS AND ROTATIONS. ROTATING FRAMES. THOMAS PRECESSION. COVARIANT FORMULATION OF PARTICLE SPIN. ELECTROMAGNETISM: INTRODUCTION TO ELECTRODYNAMICS. MAXWELL’S EQUATION. COVARIANT FORMULATION OF MAXWELL’S EQUATIONS. GAUGE TRANSFORMATIONS OF ELECTROMAGNETIC FIELDS. ELECTROMAGNETIC TENSOR. LORENTZ TRANSFORMATIONS OF ELECTROMAGNETIC FIELDS. FIELDS GENERATED BY CHARGED PARTICLES. ELECTRIC AND MAGNETIC FIELDS IN BOOSTED FRAMES. EQUATION OF MOTION OF SPIN PARTICLES IN COVARIANT FORM. COVARIANT DERIVATION OF LORENTZ EQUATION. MOTION OF PARTICLES IN A MAGNETIC FIELD. LAGRANGIAN OF THE ELECTROMAGNETIC FIELDS. MAXWELL’S EQUATIONS DERIVED IN THE LAGRANGIAN FORMALISM. ENERGY-MOMENTUM TENSOR OF THE ELECTROMAGNETIC FIELD. HAMILTONIAN OF CHARGED PARTICLES IN EXTERNAL ELECTROMAGNETIC FIELDS. WAVE EQUATIONS OF ELECTROMAGNETIC 4-POTENTIAL. SOLUTION OF WAVE EQUATIONS IN COVARIANT FORM. GREEN FUNCTIONS. ADVANCED AND RETARDED GREEN FUNCTION. CHARGED CURRENTS IN COVARIANT FORM AND THEIR INTEGRAL REPRESENTATION. LIENARD-WIECHERT POTENTIALS. RADIATION EMITTED BY A CHARGED PARTICLE. LARMOR’S FORMULA AND ITS COVARIANT GENERALIZATION. ANGULAR DISTRIBUTION OF ENERY/POWER EMITTED BY CHARGED PARTICLES. THOMAS SCATTERING. CERENKOV’S RADIATION. 2) GRAVITATION: PRELIMINARY NOTIONS: THE PARALLEL TRANSPORT OF VECTORS IN CURVED SPACETIMES. THE COVARIANT DERIVATIVE. DIFFEOMORPHISM. PROPERTIES OF TENSORS. INERTIAL AND GRAVITATIONAL MASSES. THE CONCEPT OF FORCE IN NEWTONIAN PHYSICS. EQUATIONS OF GEODESIC. CHRISTOFFEL SYMBOLS. CONNESSIONI. LOCAL INERTIAL FRAME. EQUATION OF GEODESIC DERIVED FROM THE VARIATIONAL PRINCIPLE. EQUATION OF GEODESIC DERIVED FROM GENERAL COORDINATES TRANSFORMATIONS. ACCCELERATED COORDINATED SYSTEMS. FREE FALLING REFERENCE FRAMES. THE WEAK EQUIVALENCE PRINCIPLE. RIEMANN TENSOR. RICCI TENSOR. SCALAR CURVATURE. EINSTEIN TENSOR. THE ENERGY MOMENTUM TENSOR. PROPERTIES OF THE RIEMANN AND EINSTEIN TENSOR. EINSTEIN’S FIELD EQUATIONS. WEAK FIELD APPROXIMATIONS. WAVE EQUATION FOR THE METRIC PERTUBATIONS. GRAVITATIONAL WAVES (CENNI). SCHWARZSCHILD SOLUTION. BLACK HOLE. GENERAL RELATIVITY AND ASTROPHYSICAL APPLICATIONS: GRAVITATIONAL LENSING, SHAPIRO TIME DELAY, HULSE-TAYLOR EFFECTS (GRAVITATIONAL ENERGY LOST BY BINARY SYSTEMS), GPS (CENNI). THE STANDARD COSMOLOGICAL MODEL. COSMOLOGICAL PRINCIPLE. COSMOLOGICAL EQUATION FOR THE FRIEDMANN-ROBERTSON-WALKER UNIVERSE. EQUATION OF STATE. ERAS OF THE UNIVERSE: RADIATION AND MATTER DOMINATED ERAS. THE COSMOLOGICAL CONSTANT. DARK ENERGY AND DARK MATTER (CENNI).

Contents

1) ELECTRODYNAMICS:
SPECIAL RELATIVITY. LORENTZ TRANSFORMATIONS. GENERATORS OF BOOSTS AND ROTATIONS. ROTATING FRAMES. THOMAS PRECESSION. COVARIANT FORMULATION OF PARTICLE SPIN. ELECTROMAGNETISM: INTRODUCTION TO ELECTRODYNAMICS. MAXWELL’S EQUATION. COVARIANT FORMULATION OF MAXWELL’S EQUATIONS. GAUGE TRANSFORMATIONS OF ELECTROMAGNETIC FIELDS. ELECTROMAGNETIC TENSOR. LORENTZ TRANSFORMATIONS OF ELECTROMAGNETIC FIELDS. FIELDS GENERATED BY CHARGED PARTICLES. ELECTRIC AND MAGNETIC FIELDS IN BOOSTED FRAMES. EQUATION OF MOTION OF SPIN PARTICLES IN COVARIANT FORM. COVARIANT DERIVATION OF LORENTZ EQUATION. MOTION OF PARTICLES IN A MAGNETIC FIELD. LAGRANGIAN OF THE ELECTROMAGNETIC FIELDS. MAXWELL’S EQUATIONS DERIVED IN THE LAGRANGIAN FORMALISM. ENERGY-MOMENTUM TENSOR OF THE ELECTROMAGNETIC FIELD. HAMILTONIAN OF CHARGED PARTICLES IN EXTERNAL ELECTROMAGNETIC FIELDS. WAVE EQUATIONS OF ELECTROMAGNETIC 4-POTENTIAL. SOLUTION OF WAVE EQUATIONS IN COVARIANT FORM. GREEN FUNCTIONS. ADVANCED AND RETARDED GREEN FUNCTION. CHARGED CURRENTS IN COVARIANT FORM AND THEIR INTEGRAL REPRESENTATION. LIENARD-WIECHERT POTENTIALS. RADIATION EMITTED BY A CHARGED PARTICLE. LARMOR’S FORMULA AND ITS COVARIANT GENERALIZATION. ANGULAR DISTRIBUTION OF ENERY/POWER EMITTED BY CHARGED PARTICLES. THOMAS SCATTERING. CERENKOV’S RADIATION.

2) GRAVITATION:
PRELIMINARY NOTIONS: THE PARALLEL TRANSPORT OF VECTORS IN CURVED SPACETIMES. THE COVARIANT DERIVATIVE. DIFFEOMORPHISM. PROPERTIES OF TENSORS. INERTIAL AND GRAVITATIONAL MASSES. THE CONCEPT OF FORCE IN NEWTONIAN PHYSICS. EQUATIONS OF GEODESIC. CHRISTOFFEL SYMBOLS. CONNESSIONI. LOCAL INERTIAL FRAME. EQUATION OF GEODESIC DERIVED FROM THE VARIATIONAL PRINCIPLE. EQUATION OF GEODESIC DERIVED FROM GENERAL COORDINATES TRANSFORMATIONS. ACCCELERATED COORDINATED SYSTEMS. FREE FALLING REFERENCE FRAMES. THE WEAK EQUIVALENCE PRINCIPLE. RIEMANN TENSOR. RICCI TENSOR. SCALAR CURVATURE. EINSTEIN TENSOR. THE ENERGY MOMENTUM TENSOR. PROPERTIES OF THE RIEMANN AND EINSTEIN TENSOR. EINSTEIN’S FIELD EQUATIONS. WEAK FIELD APPROXIMATIONS. WAVE EQUATION FOR THE METRIC PERTUBATIONS. GRAVITATIONAL WAVES (CENNI). SCHWARZSCHILD SOLUTION. BLACK HOLE. GENERAL RELATIVITY AND ASTROPHYSICAL APPLICATIONS: GRAVITATIONAL LENSING, SHAPIRO TIME DELAY, HULSE-TAYLOR EFFECTS (GRAVITATIONAL ENERGY LOST BY BINARY SYSTEMS), GPS (CENNI). THE STANDARD COSMOLOGICAL MODEL. COSMOLOGICAL PRINCIPLE. COSMOLOGICAL EQUATION FOR THE FRIEDMANN-ROBERTSON-WALKER UNIVERSE. EQUATION OF STATE. ERAS OF THE UNIVERSE: RADIATION AND MATTER DOMINATED ERAS. THE COSMOLOGICAL CONSTANT. DARK ENERGY AND DARK MATTER (CENNI).

	Teaching Methods
	DIRECT LECTURES WITH APPLICATIONS AND EXERCISES ON TOPIC RELATED WITH THE CONTENTS OF THE COURSE. THE AIM IS TO PROVIDE FUNDAMENTAL NOTIONS OF PHYSICS AND MATHEMATICS AIMED TO DESCRIBE NEW PHYSICS PHENOMENA, AND COLLABORATE WITH OTHER RESEARCHERS.

	Verification of learning
	ORAL EXAMINATION TO VERIFY THAT STUDENTS HAVE UNDERSTOOD THE ARGUMENTS OF THE LECTURES AND ARE ABLE TO FORMULATE AUTONOMOUS JUDGEMENTS

	Texts
	L.D. LANDAU & E.M. LIFSHITZ, "TEORIA DEI CAMPI", ED.RIUNITI J.D. JACKSON, "ELETTRODINAMICA CLASSICA", ZANICHELLI S. WEINBERG, "GRAVITATION AND COSMOLOGY", WILEY C.W. MISNER, K.S. THORNE, J.A. WHEELER, "GRAVITATION", FREEMAN & CO. R. D’INVERNO, "INTRODUCING EINSTEIN'S RELATIVITY", CLARENDON PRESS G. VILASI, "HAMILTONIAN DYNAMICS", WORLD SCIENTIFIC

	More Information
	ATTENDING TO THE COURSE IS RECOMMENDED. THE STUDENT IS INVITED TO DIRECTLY CONTACT THE PROFESSOR (ALSO IN DAYS AND HOURS NOT INCLUDED IN THE RECEPTION TIME SCHEDULE) FOR FURTHER CLARIFICATIONS OF THE ARGUMENTS OF THE PROGRAM.

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