28 research outputs found
Pullback Coherent States, Squeezed States and Quantization
No full textIn this semi-expository paper, we define certain Rawnsley-type coherent and squeezed states on an integral Kähler manifold (after possibly removing a set of measure zero) and show that they satisfy some properties which are akin to the maximal likelihood property, reproducing kernel property, generalised resolution of identity property, and overcompleteness. This is a generalization of a result by Spera. Next, we define the Rawnsley-type pullback coherent and squeezed states on a smooth compact manifold (after possibly removing a set of measure zero) and show that they satisfy similar properties. Finally, we show a Berezin-type quantization involving certain operators acting on a Hilbert space on a compact smooth totally real embedded submanifold of of real dimension , where is an open set in ℂPⁿ. Any other submanifold for which the criterion of the identity theorem holds exhibits this type of Berezin quantization. Also, this type of quantization holds for totally real submanifolds of real dimension of a general homogeneous Kähler manifold of real dimension 2 for which Berezin quantization exists. In the appendix, we review the Rawnsley and generalized Perelomov coherent states on ℂPⁿ (which is a coadjoint orbit) and the fact that these two types of coherent states coincide.The authors would like to thank Gautam Bharali (IISc, Bangalore) and Mahan Mj (TIFR, Mumbai) for the useful discussions on the theory of totally real submanifolds in several complex variables and Proposition 2.3. They would like to thank the anonymous referees for their valuable suggestions for improvement of the paper. Rukmini Dey acknowledges support from the project RTI4001, Department of Atomic Energy, Government of India, and support from grant CRG/2018/002835, Science and Engineering Research Board, Government of India
Tiffin: Memories and Recipes of Indian Vegetarian Food - Book Reading
No full textBook Reading of Tiffin: Memories and Recipes of Indian Vegetarian Food by the author Rukmini Srinivas.
Tiffin, is a delightful memoir-cum-cookbook, in which Rukmini Srinivas shares the memories and recipes of delectable food that she has cooked and eaten over many decades. Along with description of dishes, she shares stories from her childhood in British Poona, her memorable meetings with many interesting people over several decades, cooking for R. K. Narayan and her travels around the world with her husband, the renowned social anthropologist, M. N. Srinivas
© Printed in India The Weierstrass–Enneper representation using hodographic coordinates on a minimal surface
No full textAbstract. In this paper we obtain the general solution to the minimal surface equation, namely its local Weierstrass–Enneper representation, using a system of hodographic coordinates. This is done by using the method of solving the Born–Infeld equations by Whitham. We directly compute conformal coordinates on the minimal surface which give the Weierstrass–Enneper representation. From this we derive the hodographic coordinate 2 D C and its complex conjugate which enables us to write the Weierstrass– Enneper representation in a new way
A variational proof for the existence of a conformal metric with preassigned negative Gaussian curvature for compact Riemann surfaces of genus > 1
No full textGeometric prequantization of the moduli space of the vortex equations on a Riemann surface
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Erratum: “Geometric prequantization of the moduli space of the vortex equations on a Riemann surface” [J. Math. Phys. 47, 103501 (2006)]
No full textEditor: A. Kupiainen QUANTIZATION OF A DIMENSIONALLY REDUCED SEIBERG-WITTEN MODULI SPACE
No full textAbstract. In this paper we apply Quillen’s determinant line bundle construction to construct a prequantum line bundle on the moduli space of solutions N of the dimensionally reduced Seiberg-Witten equations with a Higgs field. The Quillen curvature of the line bundle is shown to be proportional to a symplectic form on the moduli space. 1
A complete conformal metric of preassigned negative Gaussian curvature for a punctured hyperbolic Riemann surface
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