My activities during the summer and winter vacations at CMI


2007


1. During July 2007 I did a summer camp in TIFR (Tata Institute Of Fundamental Research ) under the guidance of         Prof.Shiraz Minwalla. I studied various aspects of Classical Field Theory under him. Some of the main topics that I     studied were  ::

     a) non-Abelian Gauge Theory and the concept of Covariant Derivative to write Gauge invariant Lagrangians.
     b) Noether's theorem in the context of field theory and how to derive the Noether current given the symmetry               group.
     c) The concept of Solitons and Monopoles.
     d) Pursued the role of Homotopy theory in classifying Soliton solutions and its role in quantizing the flux of the               Gauge Field.
     e) Study of spontaneous symmetry breaking and the production of Goldstone Bosons via Higgs Mechanism.
     f)  Understanding the Mass Matrix for a field theory.
     g) Study of the role of Conformal Invariance in a field theory and the Poincare Group.


     For the above I mainly studied the following 3 books and lectures ::

     a) Quantum Theory of Field - II by Steven Weinberg.
     b) 2 of the Erice Lectures by Sidney Coleman from the book "Aspects of Symmetry".


2. During July 2007 , while I was at TIFR , I also studied various things in advanced Geometry under the guidance of     Prof.M.S.Raghunathan (F.R.S). I studied the following topics under him ::

     a) Metric compatible and Torsion free connections on a Riemannian Manifold.
     b) Various canonical constructions involving Principle Bundles and Vector Bundles. How there exists canonical              construction of either from the other.
     c) Connections on a Principle Bundle.
     d) Computing the Hopf Degree.


3. During May 2007 again as a part of the Physics.(Hons.) program at CMI (Chennai Mathematical Institute) I                 attended a training camp in experimental techniques in Physics at IGCAR , Kalpakkam (India Gandhi Centre for         Atomic Research ).

    During this camp I was associated to the "Ion-beam accelerator" laboratory and I studied the technique of             producing nano-clusters using the ion-impingement technique and how the clusters are characterized using the     LFRS (Low Frequency Raman Spectroscopy ) and SPR (Surface Plasmon Resonance ).

   The following is the report of my studies in the above laboratory.

   A study of nano-clusters at IGCAR,Kalpakkam.



2006

1. During December 2006 I went to attend a short series of lectures and seminars on "Developmental Biology" at NCBS ( National Center for Biological Sciences ) under the program called the "Benny Shillo course in developmental biology". The lectures introduced me to various modern frontiers of biology where techniques from differential equations and theory of dynamical systems are being used to understand the working of long range order and large scale coordination in life processes via local signalling and structuring.


2. During July 2006 I studied at SINP (Saha Institute of Nuclear Physics ) under the guidance of Prof.Krishnendu    Sengupta as a part of the Undergraduate Associateship that I was awarded by SINP. During the 1 month of camp     under him I honed my skills in various computational aspects of Quantum Theory like the following ::

    a) Computations involving Dirac matrices and Sigma matrices in the context of the Dirac Equation.
    b) Various calculations involving the precession of a spin-1/2 particle in a magnetic field.
    c) Various subteleties involving the Dirac's commutations when the Hilbert space is infinite dimensional.
    d) Non-degenerate non-relativistic Perturbation theory.

    During the above summer camp I mainly studied the following 2 texts ::

    1. Modern Quantum Mechanics by J.J.Sakurai
    2. Quantum Electrodynamics - A set of lectures by Richard Feynman at a graduate class in Caltech.

3. During June 2006 as a part of the Physics. (Hons.) course at CMI (Chennai Mathematical Institute ) I attended a      training camp in experimental techniques in Physics at HBCSE , Mumbai (Homi Bhaba Centre for Science                   Education).   

    Following are the reports of the 3 main experiments I did at HBCSE.

    Unfortunately the following documents are not of self-complete since they do not contain various circuit diagrams      and graphs which were a part of the experiment. But still it is likely that they will give a general idea to the             reader  about the content of the experiment.

     a) An experiment with transformers.
    b) An experiment to study a magnetic circuit.
    c) An experiment to study isopotential curves.




 
To be continued .....