Symposia on Theoretical Physics: 2 Lectures presented at the 1964 Second Anniversary Symposium of the Institute of Mathematical Sciences Madras, India PDF
Preview Symposia on Theoretical Physics: 2 Lectures presented at the 1964 Second Anniversary Symposium of the Institute of Mathematical Sciences Madras, India
symposia on 2 theoretical physics Contributors to this volume: A. T. Bharucha-Reid V. Devanathan H. DeWitt R. Hagedorn M. Jacob S. P. Misra A. N. Mitra F. Mohling L. O'Raifeartaigh T. K.Radha K. Raman N. R. Ranganathan S. K. Srinivasan M. H. Stone E. C. G. Sudarshan B. M. Udgaonkar R. Vasudevan K. Venkatesan B. Zumino • symposia on theoretical physics Lectures presented at the 1964 Second Anniversary Symposium of the Institute of Mathematical Sciences Madras, India Edited by ALLADI RAMAKRISHNAN Director of the Institute <±> PLENUM PRESS' NEW YORK' 1966 ISBN-13: 978-1-4684-7754-2 e-ISBN-13: 978-1-4684-7752-8 DOl: 10.1007/ 978-1-4684-7752-8 Library of Congress Catalog Card Number 65·21184 © 1966 Plenum Press Soficover reprint oft he hardcover 1st edition 1966 A Division of Plenum Publishing Corporation 227 West 17 Street, New York, N. Y.lOOll All rights reserved No part of this publication may be reproduced in any form without written permission from the publisher Introduction The second volume of this series is devoted to the Proceedings of the Second Anniversary Symposium under the chairmanship of the Niels Bohr Visiting Professor of the year - Professor L. Rosenfeld, Deputy Director of NORDITA , Copenhagen, and the Editor of Nuclear Physics. With particular appropriateness, the Symposium was inaugu rated by the Honorable C. Subramaniam, Union Cabinet Minister, the founding father of the Institute. The meeting was characterized by two features: (1) the enlargement of the scope of the discussions in theoretical physics, with the inclusion of many-body problems and statistical mechanics! (2) Seminars on pure mathematics, stimulated by the prdence and participation of Professor Marshall H. Stone of Chicago as the First Ramanujan Visit ing Professor at the Institute. The year 1963 marked a new stage in the development of high energy physics - the first successes of SU (3) symmetry and the eight fold way had such an impact on the scientific world that the hard, unyielding domain of strong interactions was now again open to ex ploration. The volume opens with two significant lectures by Sudarshan and O'Raifeartaigh on fundamental problems relating to internal sym metries. The theory of Regge poles, after its initial triumph, met with rough weather, the nature and intensity of which can be realized from the series of discussions in this volume. In statistical mechanics, we had the privilege of having with us three leading participants, Zumino of New York, Dewitt from Berkeley, and Mohling from Colorado, whose contributions to this volume sum marize their academic program during their stay at our Institute. Marshall Stone's lecture on some current trends in mathematical research was perhaps the best possible mode of initiating studies in pure mathematics at the Institute. It was followed by a systematic v vi Introduction account of semigroup methods in mathematical physics by Bharucha Reid. The seminar talk on the mathematical problems of cascade theory by Srinivasan is the first in a series on stochastic processes, the rest of which will follow in succeeding volumes. As part of the surging current of scientific literature, this volume, we hope, will convey the "integrating power of mathematics"* and the "universality of physical laws." A lladi Ramakrishnan * I am indebted for this phrase to Professor M. J. Lighthill, who referred to the role of mathematics in his inaugural lecture entitled "Waves in Fluids" on as suming the Royal Society Research Professorship in 1965. Contents Contents of Other Volumes . ix Origin of Internal Symmetries . . . . .. ......... 1 E. C. G. SUDARSHAN, University of Rochester, Rochester, New York Construction of the Invariants of the Simple Lie Groups . 15 L. O'RAIFEARTAIGH, Dublin Institute for Advanced Studies, Dublin, Ireland On Peratization Methods . 23 N. R. RANGANATHAN, Matscience, Madras, India Large-Angle Elastic Scattering at High Energies . 41 R. HAGEDORN, CERN, Geneva, Switzerland Crossing Relations and Spin States. . 55 M. JACOB, Matscience, Madras, India The Multiperipheral Model for High-Energy Processes 63 K. VENKATESAN, Matscience, Madras, India Regge Poles in Weak Interactions and in Form Factors 77 K. RAMAN, Matscience, Madras, India Effective-Range Approximation Based on Regge Poles 87 B. M. UDGAONKAR, Tata Institute of Fundamental Research, Bombay, India Some Applications of Separable Potentials in Elementary Par- ticle Physics 95 A. N. MITRA, University of Delhi, Delhi, India Form Factors of the Three-Nucleon Systems :JH and 3He 103 T. K. RADHA, Matscience, Madras, India Muon Capture by Complex Nuclei. 107 V. DEVANATHAN, University of Madras, Madras, India Electrodynamics of Superconductors 117 B. ZUMINO, New York University, New York, New York "Temperature Cutoff" in Quantum Field Theory and Mass Renormalization . 125 S. P. MISRA, Regional Engineering College, Rourkela, Orissa, India vii vW Contents Recent Developments in the Statistical Mechanics of Plasmas. 135 HUGH DEWITT, Lawrence Radiation Laboratory, Livermore, California Introduction to Quantum Statistics of Degenerate Bose Systems. 149 FRANZ MOHLING, University of Colorado, Boulder, Colorado Some Current Trends in Mathematical Research .. 159 M. H. STONE, University of Chicago, Chicago, Illinois Semigroup Methods in Mathematical Physics . 165 A. T. BHARUCHA-REID, Wayne State University, Detroit, Michigan Recent Mathematical Developments in Cascade Theory. 195 S. K. SRINIVASAN, Indian Institute of Technology, Madras, India Theory of a General Quantum System Interacting with a Linear Dissipation System 209 R. VASUDEVAN, Matscience, Madras, India Contents of Other Volumes Volume 1 Symmetries and Resonances by T. K. Radha Group Symmetries with R-Invariance by R. E. Marshak Regge Poles and Resonances by T. K. Radha On Regge Poles in Perturbation Theory and Weak Interactions by K. Raman Determination of Spin-Parity of Resonances by G. Ramachandran Pion Resonances by T. S. Santhanam Pion-Nucleon Resonances by K. Venkatesan The Influence of Pion-Nucleon Resonance on Elastic Scattering of Charged Pions by Deuterons by V. Devanathan Pion-Hyperon Resonances by R. K. Umerjee Some Remarks on Recent Experimental Data and Techniques by E. Segre On New Resonances by B. Maglic The Higher Resonances in the Pion-Nucleon System by G. Takeda ix x Contents of Other Volumes Volume 3 Many-Particle Structure of Green's Functions by K. Symanzik Broken Symmetries and Leptonic Weak Interactions by R. Oehme Partial Muon Capture in Light Nuclei by A. Fujii Quantum Gauge Transformations by J. Lukierski Theories of Particles of Arbitrary Spins by K. Venkatesan Bethe-Salpeter Equation and Conservation Laws in Nuclear Physics by W. Brenig On a Class of Non-Markovian Processes and Its Application to the Theory of Shot Noise and Barkhausen Noise by S. K. Srinivasan Volume 4 Introductory Address by V. Weisskopf A New Approach to Scattering Theory by R. Blankenbecler Conserved Vector Currents and Broken Symmetries by P. Meyer Multiplet Structure and Mass Sum Rules in the SU (6) Symmetry Scheme by V. Singh Group Representations for Complex Angular Momentum by K. Venkatesan A Model of a Unitary S-Matrix for Peripheral Interactions by K. Dietz Equivalent Potential Approach for Strong Interactions by L. A. P. Balazs "Repulsive" Potential Approach to Pion Resonances by A. N. Mitra The Renormalizability of Higher Spin Theories by J. Lukierski Muon Capture by Complex Nuclei by V. Devanathan
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