Papers by Rajaram Nityananda
arXiv (Cornell University), Dec 5, 2012
We construct the manifold describing the family of plane monochromatic light waves with all direc... more We construct the manifold describing the family of plane monochromatic light waves with all directions, polarizations, phases and intensities. A smooth description of polarization, valid over the entire sphere S 2 of directions, is given through the construction of an orthogonal basis pair of complex polarization vectors for each direction; any light beam is then uniquely and smoothly specified by giving its direction and two complex amplitudes. This implies that the space of all light beams is the six dimensional manifold S 2 ×C 2 , the Cartesian product of a sphere and a two dimensional complex vector space. A Hopf map (i.e mapping the two complex amplitudes to the Stokes parameters) then leads to the four dimensional manifold S 2 ×S 2 which describes beams with all directions and polarization states. This product of two spheres can be viewed as an ordered pair of two points on a single sphere, in contrast to earlier work in which the same system was represented using Majorana's mapping of the states of a spin one quantum system to an unordered pair of points on a sphere. This is a different manifold, CP 2 , two dimensional complex projective space, which does not faithfully represent the full space of all directions and polarizations. Following the now-standard framework, we exhibit the fibre bundle whose total space is the set of all light beams of non-zero intensity, and base space S 2 × S 2. We give the U (1) connection which determines the geometric phase as the line integral of a one-form along a closed curve in the total space. Bases are classified as globally smooth, global but singular, and local, with the last type of basis being defined only when the curve traversed by the system is given. Existing as well as new formulae for the geometric phase are presented in this overall framework.
Gravitation & Cosmology, 1988
ABSTRACT
Restricted Access. Indirect Imaging. Measurement and Processing for Indirect Imaging. Proceedings... more Restricted Access. Indirect Imaging. Measurement and Processing for Indirect Imaging. Proceedings of an International Symposium held in Sydney, Australia, August 30-September 2, 1983. Editor, J.A. Roberts; Publisher, Cambridge University Press, Cambridge, England, 1984.
Resonance, Jul 1, 2017
Earlier, he spent a decade at the National Centre for Radio Astrophysics in Pune, and more than t... more Earlier, he spent a decade at the National Centre for Radio Astrophysics in Pune, and more than two decades at the Raman Research Institute in Bengaluru. He has taught physics and astronomy at the Indian Institute of Science in Bengaluru and the IISERs in Pune and Mohali. He is keenly interested in optics in a broad sense, and more generally, problems, puzzles, paradoxes, analogies, and their role in teaching and understanding physics. Stars, other than the Sun, appear to our unaided eyes as points of light. Large telescopes show an image whose size is dictated by refractive index irregularities in the Earth's atmosphere. The size of this blurring is much greater than that of the star, and hence it is difficult to measure the stellar size. Fizeau showed how one might overcome this limitation using the two-slit interference technique. It was Michelson who carried out this programme and made the first direct measurement of the giant star Betelguse in the constellation of Orion. His value for the angular diameter, 47 milliarcseconds or 2.6 × 10 −7 radians, was completely confirmed by later work following his methods. The key concept introduced was 'fringe visibility', which turned out to be very fruitful in the later development of optics as well as astronomy.
Resonance, 2022
In this section of Resonance , we invite readers to pose questions likely to be raised in a class... more In this section of Resonance , we invite readers to pose questions likely to be raised in a classroom situation. We may suggest strategies for dealing with them, or invite responses, or both. “Classroom” is equally a forum for raising broader issues and sharing personal experiences and viewpoints on matters related to teaching and learning science.
Abstract. The broad area of galactic dynamics is presented for a physics audience, with the requi... more Abstract. The broad area of galactic dynamics is presented for a physics audience, with the requisite astronomy background in outline, and focusing on gravitational effects. The basic underlying model is a large number of particles (which could be stars or dark matter) moving in their self-consistent gravitational potential. The effects of two-particle correlations/scattering, although weak, can be cumulative and hence important for a class of systems such as star clusters which are hence termed collisional. On the larger scale of galaxies, we have collisionless behaviour which is different and in some ways richer. The basic ideas and applications in both these regimes are described, and some issues highlighted in conclusion.
Resonance, 2019
In 1909, Lewis and Tolman, then physical chemists at the Massachusetts Institute of Technology, w... more In 1909, Lewis and Tolman, then physical chemists at the Massachusetts Institute of Technology, wrote a paper which built on an earlier paper by Lewis. This gave a more mechanicsbased approach to the subject, in contrast to Einstein's original work which drew on electrodynamics. This work played a significant role in the early development of special relativity theory, then only four years old and still under heated discussion worldwide. This paper with Tolman, though a relatively minor part of Lewis's overall work, has historical and pedagogical value and gives a glimpse of his breadth, early growth and influence as a scientist. The present article outlines the arguments of their 1909 paper, and places it in context.
Resonance, 2016
Steven Vogel was a pinoneer in applying principles of mechanics to diverse living systems. This a... more Steven Vogel was a pinoneer in applying principles of mechanics to diverse living systems. This article first provides a brief overview of his career. It then reviews the concepts of Péclet number and Reynolds number which are helpful in appreciating the Classics article by Vogel reproduced in this issue.
Restricted Access. Indirect Imaging. Measurement and Processing for Indirect Imaging. Proceedings... more Restricted Access. Indirect Imaging. Measurement and Processing for Indirect Imaging. Proceedings of an International Symposium held in Sydney, Australia, August 30-September 2, 1983. Editor, J.A. Roberts; Publisher, Cambridge University Press, Cambridge, England, 1984.
Bulletin of The Astronomical Society of India, 1978
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Papers by Rajaram Nityananda