ABOUT THE COURSE:This course is geared towards providing a microscopic basis for wave dispersion and propagation. As a part of recapitulation, one would derive the dispersion relations for a wave propagation followed by that the types of polarization, polarization angle and ellipticity angle would be worked out. Following this, the microscopic theory of wave propagation and dependence of the wave parameters on medium composition will be shown. These will be shown using the finiteness of the photon two point function or the polarization tensor. We would take recourse to established tools of finite temperature quantum field theory and the theorems established there off (Furrys theorem) to show the finiteness of the parity P violating part of the photon polarization tensor. Faraday effect would be introduced as a sequel to this discussion. Being armed with these fudamental tools, we would introduce the concepts of coherency matrix and find out the Stokes parameters from there. We would show how these parameters vary under rotation about the direction of wave propagation. From there we will identify the invarians parameters of polarization description. We would conclude by identifying the possible terrestial and celestial applications of this formalism.INTENDED AUDIENCE: Bachelor’s final Masters first Semester.PREREQUISITES: Mathematical Methods in Physics, Basic Electromagnet theory and statistical mechanicsINDUSTRY SUPPORT: We have not explored this aspects of it at the moment
Overview
Syllabus
Week 1: Isotropy and Homogeneity of space and time.Translation symmetry in space and time. The discrete symmetries like time and space reversal symmetry. Charge conjugation symmetry. The metric tensor and the levi-civita tensor and their behavior under the discrete transformations. Constituents of a media and the 4 velocity vector and their modification under these symmetry transformations.Week 2:Type of excitations scalar, vector and tensor.Principle of invariance and covariance of the equations of motions. Maxwells equations and the derivation of the electromagnetic equations of motions. Introduction to scalar and vector potentials. Solutions of Electromagnetic equations of motions in terms of vector potentials in vacuum and in a medium. Medium dependence of the dispersion relations. Phase velocity and group Velocity. Linear circular and elliptic Polarization. Plane of polarization, Polarization angle and Ellipticity angle. Rotation of plane polarization and optical activity.Week 3:Introduction to microscopic theory of wave propagation. The natural basis vectors in a finite density medium. Introduction to the Polarization tensor (two point function). Role of photon polarization tensor Πμ,ν(k, T, μ) on wave propagation. The longitudinal and the transverse components of the Polarization tensor. Their expansion in the tensorial basis and the form factors. The expression of the form factors for norelativisic, relativistic and degenerate media. Furrys theorem. General expression of the two point function in a magnetized media from symmetry arguments.The parity (P) violating nature of the same. Rotation of the plane of polarization of electro-magnetic fields, when passing through a media that is charge asymmetric and odd in powers of external magnetic field. The Faraday Rotation and physical condition on the media to have Faraday rotation.Week 4:The coherency matrix. Behavior of the same under rotation about an axis. The stokes variables Q, U and V. Their relation to the elements of the coherency matrix. Discussions of elliptical, circular, linear polarizations in terms of the stokes parameters. Defining the degree of linear polarization using stokes parameters. Description of Polarization angle and ellipticity angle in terms of Stokes Parameters . Constructing the invariants of polarization variables under rotation from Stokes parameters. Extraction of medium properties from the polarization parameters. Application of same in astrophysical situations.
Taught by
Prof.Avijit K. Ganguly
