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1988 Cern School of Physics Proceedings CERN 914)1 10 January 1991 ORGANISATION EUROPÉENNE POUR LA RECHERCHE NUCLÉAIRE CERN EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH 1988 CERN SCHOOL OF PHYSICS Lefkada, Greece 8 September - 1 October 1988 PROCEEDINGS GENEVA 1991 \ Propriété littéraire et scientiOt]iie réservés pour Literary and scientific copyrights reserved in ail tous les pays du monde. Ce document ne peut countries of the world, This report, or any part être reproduit ou Iradin! en (oui (ju en partie of it. may- not be reprinted or translated without iaiu l'autorisation écrite du directeur gênerai du written permission or the copyright holder, the CERN, titulaire du droit d'auteur. Dans les cas Director-tîcneral or CERN, However, permis­ appropriés, cl s'il s'ap,it d'utiliser ttî document à sion will be freely granted for appropriate des fins non commerciales, ecllc autorisation non-Lommereial use, sera volontiers accordée. II' any patentable invention or registrable design Le CERN ne revendique pas la propriété des is described in the report, CERN makes no claim inventions brevetabJes et dentins on mode let to properly rights in il but offers it for the free susceptibles de dépôt qui pourraient être décrits use of research instilullons, manufacture]' and dans le présent document; ceux-ci peuvent être others. CERN, however, may oppose any librement utilisés par tes instituts de recherche, attempi by a user 10 daim any proprietary or les industriels et autres intéressés. Cependant, le patent rights m such inventions or designs as CERN se réserve le droit de s'opposer à toute may be described in (he present document. revendication qu'un usager pourrait faire de la propriété scientifique ou industrielle de toute invention et tout dessin ou modèle décrits dans le présent document, ISSN 0531-4283 ISBN 92-9083-032-8 CE RN 91-01 10 January 1991 ORGANISATION EUROPÉENNE POUR LA RECHERCHE NUCLÉAIRE CERN EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH 1988 CERN SCHOOL OF PHYSICS Lefkada, Greece 8 September - 1 October 1988 PROCEEDINGS GENEVA 1991 CERN-Service d'information scientifique-RD/815-- 700-mars 1991 1000-novembre 1991 ABSTRACT PREFACE The CERN School of Physics is intended to give young The 1988 CERN School of Physics was held from 18 September to 1 October on the experimental physicists an introduction to the theoretical aspects beautiful and unspoilt island of Lefkada off the west coast of Greece, It was attended by or recent advances in elementary particle physics. These 106 students; all but four came from laboratories or institutes in the CERN Member Proceedings contain reports of lecture series on the following States. topics: introduction to field theory and to weak interactions, heavy icn collisions, perturbative QCD, the standard model, proton- Our sincere thanks are due to the lecturers and discussion leaders for their active antiproton collider results and detectors, cosmology. participation m the School and for making the scientific programme so stimulating. The high attendance at the lectures in spite of the warm and sunny weather testifies to the excellence of their work. The School was organized by CERN in conjunction with the Nuclear Research Center 'Demokritos', Athens, and we are indebted to the Center and particularly to the Scientific Director, Professor N. Antoniou, for financial support. Our warmest thanks are extended to Dr. E.N. Argyres ('Demokritos') who, as Director of the School, ensured the smooth running of all the essential practical details of the day-to-day organization. Our particuiar thanks go also to his wife, Antigone, for her untiring efforts, especially for the liaison with the photocopy shops, and for her ever-cheerful disposition. Dr. Argyres was ably assisted by his Greek colleagues on the Organizing Committee, Dr. G.K. Leontaris of the University of Ioánnina and Dr. N. Tracas of the Technical University of Athens who competently handled ail the financial matters. Lastly, the CERN Organizing Secretary, Miss S.M. Tracy, efficiently co-ordinated all the preparations for the School. The School was head in the Xenia Hotel, Lefkada, and our thanks go to the Manager, Mr. E. Vagenas and his staff for making us welcome and comfortable. The evening meal was taken in the Restaurant 'Adriatica' in Lefkada, thus giving the participants the chance to walk through the charming old town before dinner, when the social life was most active. The owner, Mr. A. Argyris, spared no efforts to meet the healthy appetites and tastes of the multi-national student body, who greatly enjoyed his hospitality. A varied social programme was organized by Dr. Argyres, with the aid of his friends and colleagues of his home town, especially the Mayor, Mr. E. Margelis. The School ended with a farewell banquet, attended by Professor Antoniou, Director of NCSR 'Demokritos', Professor H. Schopper, the Director-General of CERN, Mr. P. Valakis, the County authority, the Mayor of Lefkada, and the Right Reverend Nikiforos, Lord Bishop of Lefkada, amongst others; it was enlivened by a spirited folklore performance by the 'Orpheus' dancers of Lefkada. W.O. Lock on behalf of the CERN Organizing Committee Ji ! ".» . CONTENTS Page Preface, WO. Lock iv Elementary field theory, G. Tiktopoulos 1 Phenomenology of electroweak interactions, G. Altarelii 51 Heavy ion collisions, W. Willis 101 QCD and collider physics, W.J. Stirling (Lecture notes by R.K. Ellis and W.J. Stirling/ 135 Beyond the Standard Model, D.V. Nanopouhs 237 Collider experiments, P. Jenni 297 Particle physics and cosmology, G. Lazarides 353 Organizing Committee 379 List of Participants 380 ELEMENTARY FIELD THEORY or, equivalently, the time development of state vectors in the Schrôdinger picture according to G. Tiktopoulos National Technical University Athens, Greece 1.3 The path integral The main dynamical problem for the quantum system is: given that at time t = ti, q = qi (i.e. the system is in an eigenstate of q with eigenvalue qi), what is the amplitude that at a later time t = t2 one will measure q to be equal to q ? We can write this amplitude as LECTURE ONE: FIELDS AND PARTICLES e In this lecture we introduce the method of path integrals and use it to calculate the Green's <*.Mvt.> „-<i.|e-Ht,'-*,*V>. functions first for the "driven harmonic oscillator" and then for the "free real scalar field". H1 ScHRot) 1.1 Action principle in classical mechanics Consider a simple system with one degree of freedom described by the Lagrangian (q = dq/dt) Ordinarily, it is obtained by solving the Schrôdinger equation as a differential equation. Here, we will express it as a. path integral, a remarkably fruitful way of writing amplitudes. From the completeness of the eigenstates |q,t) at any time t we deduce the "reproducing property" A classical trajectory q(t) makes the action A = J«Jt L(^4; stationary, i.e. Dividing the time interval (t,t') into a large number N of equal intervals (t,ti), (ti.tz), (tN- i,t') we write This is the differential equation of motion. In our case For small time intervals we may use the approximation (see Appendix) 1.2 Canonical quantization To quantize the simple system of Section 1.1 (i.e. to construct a quantum system which in the classical limit ti—• 0 goes over to the system of Section 1.1) we introduce the canonical momentum p conjugate to the coordinate q which allows us to write and we express the quantity qp - L, the energy, as a function of q and p A -, i(A* •AH/H.,+ -+Avyt We go over to the quantum system by postulating that q and p are operators obeying the (equal where time) commutation relation In-cl-^ k.K-i - L(^pV(^) et and that the Hamiltonian H = p /2m + V(q) represents the energy operator. Recall that H determines the time development of operators in the Heisenberg picture according Since the sum £k Ak.k- I in the exponent would approximate the classical action if q, qi to q„- l, q' lay on a smooth trajectory we write this, symbolically, i'A(l>/k <V/fv>H =iW 1 2 3 4 For this problem an important quantity is <Q+ |ii )j = the probability amplitude for the (Heisenberg picture) ground state |Q~) at t = - T < - Ti to go into the ground state |t!+ ) at t = T > T! in the presence of J(t). 1 The path integral form for (q',t'|q,t) is valid even when the potential V(q) depends on time. Therefore, if ^o(q) is the ground-state wave function of the oscillator we have O^ N :ii»i€ One way to calculate is to expand the path integral in powers of J: as an integral over all "paths" i.e. classical trajectories from (q,t) to (q',t'). This is the famous path integral introduced by Feynman (1948). <fi*ur> -<.orui"x „ + Note that in the limit h -» 0 the factor elA/* oscillates rapidly so that the paths for which A is iA stationary dominate. But for those paths 5A/5q = 0, i.e. they are the classical trajectories. Thus the r r * -TtA ^trA path integral approach explains in the most direct way the passage to classical physics in the limit fi->0. 1.4 The driven harmonic oscillator For the simple harmonic oscillator of frequency w and mass = 1 (from now on we set h = 1) we have: L = - -^ l tl r1 > P-1 •je '** ^je " <j(ge ' 9(trtj + The Hamiltonian is "diagonalized" by introducing the ladder operators a and af according to The first term in this expansion equals one, since in the absence of J we have il* = il ~, whereas the second term vanishes because the integrand is odd in q(ti).
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