Symposia on Theoretical Physics and Mathematics: 7 Lectures presented at the 1966 Summer School of the Institute of Mathematical Sciences Madras, India PDF
Preview Symposia on Theoretical Physics and Mathematics: 7 Lectures presented at the 1966 Summer School of the Institute of Mathematical Sciences Madras, India
symposia on 7 theoretical physics and mathematics Contributors to this volume: P. L. Kannappan A. N. Mitra F. Pham G. Rickayzen M. Scadron S. K. Singh S. K. Srinivasan B. M. Udgaonkar • symposia on theoretical physics and mathematics Lectures presented at the 1966 Summer School of the Institute of Mathematical Sciences Madras, India Edited by ALLADI RAMAKRISHNAN Director of the Institute ~ PLENUM PRESS. NEW YORK • 1968 ISBN-13: 978-1-4684-7729-0 e-ISBN-13: 978-1-4684-7727-6 DOl: 10.1007/ 978-1-4684-7727-6 Library of Congress Catalog Card Number 65-21184 © 1968 Plenum Press Softcover reprint of the hardcover 1st edition 1968 A Division of Plenum Publishing Corporation 227 West 17 Street, New York, N. Y. 10011 All rights reserved No part of this publication may be reproduced in any form without written permission from the publisher. Introduction This volume contains the proceedings of the Third Matscience Summer School held at Bangalore in September, 1966. The special feature of these proceedings was two systematic series of lectures, one by F. Pham of C.E.N., Saclay and CERN, Geneva and the other by G. Rickayzen of the University of Kent, Canterbury. Pham dwelt at length on the applications of the methods of alge braic topology and differential forms to the study of the analytic properties of S-matrix theory, in particular, with reference to the location of singularities of the multiple scattering processes. This exposition was a natural sequel to the lectures of V. L. Teplitz, pub lished in an earlier volume of this series. Rickayzen discus.sed in detail the latest theory of superconductivity. Other lectures were those of Scadron, who dealt with some formal features of potential scattering theory, and B. M. Udgaonkar and A. N. Mitra, who spoke on certain aspects of bootstraps and quark models, respectively. The contributions in pure mathematics in this volume include two lectures by S. K. Singh, one on the field of Mikusinski operators and another on Riemann mapping theorem, and a lecture on cosine func tionals by P. L. Kannappan. One of the highlights of the symposium was a lecture by S. K. Srinivasan who is keeping alive the interest of the Madras group in the theory of stochastic processes and who, in particular, has enlarged the domain of the application of the theory of product densities. Alladi Ramakrishnan v Contents Contents of Other Volumes .................................. ix Superconductivity ........................................... 1 G. RICKAYZEN, University of Kent, Canterbury, England Singularities of Multiple Scattering Processes .................. 17 F. PHAM, C.E.N., Saclay, France Some Notions of Local Differential Topology .................. 65 F. PHAM, C.t.N., Saclay, France Formal Aspects of Potential Theory. ........................ 101 M. SCADRON, Imperial College of Science and Technology, London, England Some Simple Bootstrap Models ............................. 117 B. M. UDGAONKAR, Tata Institute of Fundamental Research, Bombay, India Quark Model for Baryons and Resonances ................... 131 A. N. MITRA, University of Delhi, Delhi, India Riemann Mapping Theorem ................................ 139 S. K. SINGH, Karnatak University, Dharwar, India Field of Mikusinski Operators .............................. 145 S. K. SINGH, Karnatak University, Dharwar, India On the Cosine Functional Equation .......................... 153 P. L. KANNAPPAN, University of Waterloo, Waterloo, Canada A Novel Approach to the Kinetic Theory of Fluids- Onset of Turbulent Motion ............................... 163 S. K. SRINIVASAN, Indian Institute of Technology, Madras, India Author Index ............................................. 187 Subject Index ............................................. 189 vii Contents of Other Volumes VOLUME 1 Symmetries and Resonances Pion-Nucleon Resonances T.K. Radha K. Venkatesan The Influence of Pion-Nucleon Group Symmetries with R-Invariance Resonance on Elastic Scattering R. E. Marshak of Charged Pions by Deuterons Regge Poles and Resonances V. Devanathan T.K. Radha Pion-Hyperon Resonances R. K. Umerjee On Regge Poles in Perturbation Theory and Weak Interactions Some Remarks on Recent Experimental K. Raman Data and Techniques E. Segre Determination of Spin-Parity On New Resonances of Resonances B. Maglic G. Ramachandran The Higher Resonances in the Pion Resonances Pion--:Nucleon System T. S. Santhanam G. Takeda VOLUME 2 Origin of Internal Symmetries Some Applications of Separable E. C. G. Sudarshan Potentials in Elementary Particle Construction of the Invariants of the Physics Simple Lie Groups A. N. Mitra L. O'Raifeartaigh Form Factors of the Three-Nucleon On Peratization Methods Systems H3 and He3 N. R. Ranganathan T.K.Radha Large-Angle Elastic Scattering at Muon Capture by Complex Nuclei High Energies V. Devanathan R.Hagedorn Electrodynamics of Superconductors Crossing Relations and Spin States B.Zumino M. Jacob "Temperature Cutoff" in Quantum The Multiperipheral Model for Field Theory and Mass High-Energy Processes Renormalization K. Venkatesan S. P. Misra Regge Poles in Weak Interactions and Recent Developments in the Statistical in Form Factors Mechanics of Plasmas K. Raman H. DeWitt Ix Contents of Other Volumes Effective-Range Approximation Based Introduction to Quantum Statistics of on Regge Poles Degenerate Bose Systems B. M. Udgaonkar F. Mohling Some Current Trends in Mathematical Recent Mathematical Developments in Research Cascade Theory M. H.Stone S. K. Srinivasan Theory of a General Quantum System Semi group Methods in Mathematical Interacting with a Linear Dissipation Physics System A. T. Bharucha-Reid R. Vasudevan VOLUME 3 Many-Particle Structure of Green's Theories of Particles of Arbitrary Spins Functions K. Venkatesan K. Symanzik Bethe-Salpeter Equation and Broken Symmetries and Leptonic Conservation Laws in Nuclear Weak Interactions Physics R.Oehme W. Brenig On a Class of Non-Markovian Partial Muon Capture in Light Nuclei Processes and Its Application A. Fujii to the Theory of Quantum Gauge Transformations Shot Noise and Barkhausen Noise J. Lukierski S. K. Srinivasan VOLUME 4 Introductory Address "Repulsive" Potential Approach to V. Weisskopf Pion Resonances A New Approach to Scattering Theory A. N. Mitra R. Blankenbecler The Renormalizability of Higher Conserved Vector Currents and Spin Theories Broken Symmetries J. Lukierski Ph. Meyer Muon Capture by Complex Nuclei V. Devanathan Multiplet Structure and Mass Sum Rules in the S U ( 6) Symmetry Comments on Sum Rules Scheme P. T. Landsberg and D. J. Morgan V. Singh Inelastic Neutron Scattering and Group Representations for Complex Dynamics in Solids and Liquids Angular Momentum A. SjOlander K. Venkatesan Axioms and Models A Model of a Unitary S-Matrix for M. H. Stone Peripheral Interactions Characters of Semi-Simple Lie Groups K. Dietz Harish-Chandra Equivalent Potential Approach for Sequent Correlations in Evolutionary Strong Interactions Stochastic Point Processes L. A. P. Balazs S. K. Srinivasan Contents of Other Volumes xi VOLUME 5 Lectures on Nested Hilbert Spaces On the Conformal Group and its A. Grossmann Equivalence with the Hexa dimensional Pseudo Euclidean Elementary Homology Theory Group N. R. Ranganathan M. Baktavatsalou Application of Algebraic Topology Certain Extremal Problems to Feynman Integrals K R. Unni V. L. Teplitz Fluctuating Density Fields and Weak Interactions Fokker-Planck Equations R. J. Oakes S. K Srinivasan Fundamental Multiplets Contraction of Lie Groups and Lie Algebras A. Ramakrishnan K Venkatesan The Ground States of He3 and H3 A Pattern in Functional Analysis K Ananthanarayanan J. L. Kelley Remarks of the Present State of Correspondence Principles in General Relativity Dynamics S. Kichenassamy R. Arens VOLUME 6 On Locally Isomorphic Groups Functions of Exponential Type and Cartan-Stiefel Diagrams K R. Unni B. Gruber A Model for Processing Visual Data Linear Response, Bethe-Salpeter with Applications to Bubble Equation, and Transport Coefficients Chamber Picture Recognition L. Picman (Summary) The Description of Particles of R. Narasimhan Arbitrary Spin P. M. Mathews On Functional Methods in the S-Matrix Theory Radiative Corrections in ,B-Decay J. Rzewuski G. Klillt:n What Are Elementary Particles An Impact Parameter Formalism Made Of? T. Kotani E. C. G. Sudarshan Some Properties of the Recent Developments in Cosmology Fourier-Bessel Transform J. V. Narlikar G. Klillen An Introduction to Nevanlinna Theory The Al and K** (1320) W. KHayman Phenomena-Kinematic Normalization of Bethe-Salpeter Enhancements of Mesons? Wave Functions G. and S. Goldhaber Y. Takahashi The Photoproduction and Scattering Non-Lagrange Theories and of Pions from H3 and Hell Generalized Conservation K Ananthanarayanan Y. Takahashi Cosmic X-Rays, y-Rays, and Electrons Relativistic Extensions of SU(6) R. R. Daniel H. Ruegg ,B-Decay and wCapture Coupling A Survey of -;r-N Scattering, and of Constants the T=Yz Amplitudes S. C. K Nair B. J. Moyer xii Contents of Other Volumes VOLUME 8 A General Outlook on the Problem Muon Capture as a Probe for Nuclear of Quasars Structure N. Dallaporta M.Rho Functional Differential Equations On the Unification of Physical S. G. Deo Theories A. Mercier On Some Convex Functions and Related Inequalities A Note on the Representations of C. J. Eliezer Dirac Groups A. Ramakrishnan and On Harmonic Differential Forms in a I. V. V. Raghavacharyulu General Manifold N. Prakash Relativistic Wave Equations for Developments in the Theory of Higher Spin and Their Quantization Univalent Functions P. M. Mathews K. S. Padmanabhan Generalized Analytic Continuation Contributions to the Relativistic Gen H. S. Shapiro eralization of the Kinetic Theory of Gases and Statistical Mechanics Congruent Embedding into Boolean I. I. Horvath Vector Spaces N. V. Subrahmanyam Variational Methods in Scattering Raikov Systems Theory J. H. Williamson C. I. Ioachain Certain Problems in the Design of The (1T + ,2p) Reactions on Nuclei Programmed-Motion Systems T. Bressani et al. A. S. Galilulin
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