Talks and writeups
|Name||Seminar 1||Seminar 2|
|Argha Banerjee||[abs] Super-luminal motion||Fourier analysis (3) 27/9 (Mo)|
|Suryanarayan Dash||[abs] Spinors||Delta functions 28/9 (Tu)|
|Anindya Dey||[abs] Spinors||Multipole moments 1/10 (Fr)|
|Aditya Gilra||[abs] Lorentz inavariance||Causality (1) 23/9 (Th)|
|Partha Nag||[abs] Lorentz invariance||Permutation irreps (2) 25/9 (Sa)|
|Naren H.R.||[abs] Horizon problem||Causality (2) 24/9 (Fr)|
|Aseem Paranjape||[abs] Super luminal motion||Causality (3) 25/9 (Sa)|
|Swapnil Patil||[abs] Lorentz invariance||Permutation irreps (1) 25/9 (Sa)|
|Bhargava Ram||[abs] Spinors||Fourier analysis (1) 24/9 (Fr)|
|Shamayita Ray||[abs] Horizon problem||Fourier analysis (2) 27/9 (Mo)|
|Tridib Sadhu||[abs] Lorentz invariance||Potential problems 23/9 (Th)|
The first round of seminars
General instructions for the submissions
As part of the talk, submit a one page writeup (each) on the material that you covered, with sufficient detail that you think anyone else in your class would be able to follow and work out the remaining detail by themselves.
When more than one person has shared the topic, divide up the material logically, so that each person's submission is complete in itself, but gains in depth when read with the others'. Appropriate division of work is an important skill set in science, called collaborative skills.
A page will be defined as one side of an A4 sheet, with the default article style of LaTeX. Your submission will be part of the general pool of study material for everyone in the course.
Aseem should mention (and give references to) the various examples of fake superluminal motion that he listed. The example of jets in AGN should be given in some detail.
Argha should give references to the so-called X-wave experiments, and the reason why this is fake propagation faster than light. Do either of you know the EPR paradox? Does the X-wave stuff have any analogy with that? If you don't know EPR then don't spend too much time on it.
Tests of Lorentz Invariance
The material should explain what the RMS framework is, and which parameters can be constrained by which experiments. The talks concentrated on Michelson-Morley, Kennedy-Thorndike and clock comparison experiments. Is the Ives-Stilwell experiment redundant? Give references as appropriate. Are you aware of the paper H.P.Robertson, Rev. Mod. Phys. 21, 378, 1949? It might be useful.
Please pay closer attention to the fact that the earth is a non-inertial frame, and therefore there must be corrections to earth based observations which have to be taken into account when testing Lorentz invariance.
The Horizon Problem
The material should explain what the horizon problem is, with sufficient detail for the explanation, but only the necessary detail. You need only mention the inflationary solution without giving details. Give references as appropriate. Divide up the material between the two of you logically, so that each person's submission is complete in itself, but gains in depth when read with the other's.
The submission should contain the material covered in the talk, as well as answers to the main questions asked; ie, why the metric is antisymmetric, and how do you construct a multi-index spinor which transforms as a 4-vector.
The second round of seminars
Each person will have to give a 1 hour seminar and prepare and submit a writeup of 4 pages (LaTeX, default article style) within a week of presenting the seminars. Abstracts for each seminar must be submitted by Sunday, September 12 (usual method: as a readable ps or pdf file, with references, and by mail with receipt date stamp on or before the due date). When more than one person is involved in a given topic, it is the group's job to coordinate the presentations and writeups such that they together cover the whole subject.
- Construction of the multipole moments of a static charge distribution
in terms of the spherical harmonics. Their usefulness in defining the
electric field strength. Consideration of the multipole moments and
the resulting fields as rotational tensors. (Anindya Dey)
Starting point: See the follow up questions for day 6. Also, G. Arfken, "Mathematical methods for physicists" sections 4.10 and 4.11.
- Complex analyticity and harmonic functions. Their use in solving Laplace's equations in a plane. Using conformal mappings to transform electrostatic problems. (Tridib Sadhu) Starting point: J.D. Jackon "Classical Electrodynamics", Panofsky and Phillips, chapter 4, and any book on complex analysis.
- Delta functions as limits of regular functions. Functions defined
as integrals and derivatives of the delta function. Fourier
transform of a delta function as a limit, and the uncertainty principle.
Starting point: G. Arfken, "Mathematical methods for physicists" section 8.7. Also, Schiff, "Quantum Mechanics", Chapter 11.
- Constructing all irreducible representations for the group of
permutations of three objects, and using them to write down rank 3
tensors with all possible symmetries under permutations of the
indices. Generalization to tensors of higher rank.
(Partha Nag and Swapnil Patil)
Starting point: G. Arfken, "Mathematical methods for physicists" section 4.9. Also, M. Tinkham, "Group theory and quantum mechanics".
- Fourier analysis as a study of representations of the group of
translations. Its applications to solving linear partial differential
equations with specific boundary conditions and symmetries. Breaking
of translational invariance, Brillouin zone formation and the
corresponding solutions of partial differential equations.
(Argha Banerjee, Bhargava Ram and Shamayita
Starting point: G. Arfken, "Mathematical methods for physicists" chapters 14 and 15. Also, M. Tinkham, "Group theory and quantum mechanics", Ashcroft and Mermin, chapters 8 and 9. The handbook by Abramowicz and Stegun provides quick references to properties of special functions, but for more details you have to look elsewhere.
- Causality and the relation between dispersion and absorption of
signals. (Aditya Gilra, Naren H.R. and Aseem Paranjape)
Starting point: G. Arfken, "Mathematical methods for physicists" section 7.3 and all 3 references there; also section 15.7. Article by J.S. Toll, Rev. Mod. Phys., 104 (1956) 1760.
- Sunday, September 12, 2004
- Deadline for the first submission of the abstract in ps or pdf form
- Talks as in the table above
- Talks are to be strictly of one hour's duration (sudden death rules). 5 minutes for questions.
- Friday, October 8, 2004
- Writeups: 4 pages of LaTeX default article style (10 pt), including figures and references.
© Sourendu Gupta. Created on Sep 02, 2004. Last updated on Sep 21, 2004.