DOCSLIB.ORG

Introduction to Physics of Elementary Particles

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Introduction to Physics of Elementary Particles INTRODUCTION TO PHYSICS OF ELEMENTARY PARTICLES INTRODUCTION TO PHYSICS OF ELEMENTARY PARTICLES O.M. BOYARKIN Nova Science Publishers, Inc. New York c 2007 by Nova Science Publishers, Inc. All rights reserved. No part of this book may be reproduced, stored in a retrieval system or transmitted in any form or by any means: electronic, electrostatic, magnetic, tape, mechanical photocopying, recording or otherwise without the written permission of the Publisher. For permission to use material from this book please contact us: Telephone 631-231-7269; Fax 631-231-8175 Web Site: http://www.novapublishers.com NOTICE TO THE READER The Publisher has taken reasonable care in the preparation of this book, but makes no expressed or implied warranty of any kind and assumes no responsibility for any errors or omissions. No liability is assumed for incidental or consequential damages in connection with or arising out of information contained in this book. The Publisher shall not be liable for any special, consequential, or exemplary damages resulting, in whole or in part, from the readers’ use of, or reliance upon, this material. Independent verification should be sought for any data, advice or recommendations contained in this book. In addition, no responsibility is assumed by the publisher for any injury and/or damage to persons or property arising from any methods, products, instructions, ideas or otherwise contained in this publication. This publication is designed to provide accurate and authoritative information with regard to the subject matter cover herein. It is sold with the clear understanding that the Publisher is not engaged in rendering legal or any other professional services. If legal, medical or any other expert assistance is required, the services of a competent person should be sought. FROM A DECLARATION OF PARTICIPANTS JOINTLY ADOPTED BY A COMMITTEE OF THE AMERICAN BAR ASSOCIATION AND A COMMITTEE OF PUBLISHERS. Library of Congress Cataloging-in-Publication Data Available upon request ISBN 978-1-60692-598-0 Published by Nova Science Publishers, Inc. New York In the textbook all the known types of fundamental interactions are considered. The main directions of their unification are viewed. The basic theoretical ideas and the basic exper- iments, which allow to establish a quark-lepton level of a matter structure, are discussed. The general scheme of building up the theory of interacting fields with the help of the local gauge invariance principle is given. This scheme is used under presentation of the basic aspects of the quantum chromodynamics and the electroweak theory by Weinberg-Salam- Glashow. Principles of operation and designs of accelerators, neutrino telescopes, and ele- mentary particle detectors are considered. The modern theory of the Universe evolution is described. The textbook is primarily meant for Physics Department students. The book also will be useful to teachers, researches, post-graduate students and to all who are interested in problems of a modern physics. Contents Preface xi 1 Interactions and Ways of Their Unification 1 1.1.StrongInteraction............................... 1 1.2.ElectromagneticInteraction.......................... 4 1.3.WeakInteraction............................... 5 1.4.GravitationInteraction............................ 7 1.5. Grand UnifiedTheory............................. 12 1.6.Supersymmetry................................ 16 1.7.Supergravitation................................ 17 1.8.Kaluza-KleinTheory............................. 17 1.9.SuperstringTheory.............................. 20 2 Three Steps of Quantum Stairway 23 2.1.AtomicTheory................................ 23 2.2.NuclearModelofAtom............................ 25 2.3.Proton-NeutronModelofAtomNucleus................... 33 3 Leptons and Hadrons 37 4 Periodic Table of Hadrons 43 4.1. Yukawa Hypothesis .............................. 43 4.2.FeynmanDiagrams.............................. 48 4.3.ElementsoftheGroupTheory........................ 51 4.4. Isotopic Multiplets .............................. 62 4.5.Resonances.................................. 71 4.6. Unitary Multiplets ............................... 77 4.7. SU(3)-Symmetry............................... 82 5 Quark-Lepton Level of Matter Structure 95 5.1.Quark”Atoms”................................ 95 5.2.ElasticFormfactorsofNucleons.......................100 5.3.BjorkenScaling................................118 5.4.PartonModel.................................123 5.5.Color.....................................126 ix x Contents 5.6. c-Quark and SU(4)-Symmetry........................135 5.7. b and t-Quarks................................139 5.8. Looking for Free Quarks ...........................143 6 Standard Model 147 6.1.AbelianGaugeInvarianceandQCD.....................147 6.2.NonabelianGaugeInvarianceandQCD...................151 6.3. Spontaneous Symmetry Breaking. Higgs Mechanism . ...........153 6.4.Weinberg-Salam-GlashowTheory......................158 7 Fundamental Particles 173 8 Devices of Elementary Particle Physics 181 8.1. Particle Accelerators .............................181 8.2.ParticleDetectors...............................190 8.3.NeutrinoTelescopes..............................195 9 Macroworld 201 9.1.ModelsofUniverseEvolution........................201 9.2. Neutrino Astronomy .............................223 Epilogue 229 Appendix 231 References 233 Index 235 Preface The history of Physics is as abundant in shocks as a political life of a typical banana re- public, where babies learn the word ”revolution” immediately after the word ”mama”. At quiet times, however, physicists often have the illusion of complete understanding of the world. It was also the case in the beginning of the XXth century, when in the clear skies of Classical Physics there were only two small clouds, two unsolved problems, namely ether hypothesis and radiation spectrum of blackbody. The results of experiments by Mickelson and Morlet demonstrated that ether possesses no observable properties. They did not only ruin the ether theory altogether, but they also made the foundation of the special theory of relativity (STR), created by Einstein in 1905. In our opinion, there are two following aspects of the STR which form nowadays an education standard of any physicist and that is the highest price for any physical theory. The former aspect deals with understanding of properties belonging to the four dimensional space-time that surrounds us. The latter one reflects a deep faith in worldly wisdom of a correspondence principle, which reads: every new and more precise theory comprises in the utmost case the old and less exact theory. Thus, Newton’s classical mechanics was not wrong it simply turned out to be approximate theory. It is easy to check, that all of its formulae can be obtained from the corresponding expressions in the STR at passage to the limit c → ∞. When describing relativistic phenom- ena (v ∼ c), the correct answer can be given by the STR only. Max Plank’s explanation of radiation spectrum of blackbody was that very spark to stroke the flames of the second revo- lution in Physics which resulted in creation of non-relativistic quantum mechanics (NQM). This theory explained a matter structure at atomic and molecular levels with striking suc- cess. The Planck constant, the action quantum, plays the fundamental role in the NQM. As soon as any dynamic observables of the system having action dimension (energy×time) are comparable in their value with , classical physics ends in a fiasco and the right description can be obtained only within the NQM. Once again we can check, that familiar formulae of classical physics follow from their counterparts of the NQM at passage to the limit → 0. In 1915 Einstein’s general theory of relativity (GTR) succeeded classical theory of grav- itation. The GTR made a revolution both in methods and in the very contents of theoretical physics. Einstein discovered not only the new physical laws, but a new method of establish- ing the new laws as well. The GTR was based on the equivalent principle which suggested no difference between gravitation and acceleration in a small spatial domain. Unlike New- ton’s theory of gravitation, the GTR is not only a theory of gravitational interaction, but also a theory of space-time, consequently, a theory of the Universe in general. Non-stationary models of the Universe, obtained by Friedmann on the basis of the GTR equation solutions xii O.M. Boyarkin at that time seemed to be mere fantastic. However, as soon as 1929 astronomical obser- vations by A. Hubble proved the theory of the expanding Universe to be right. Thus, the Universe of Plato and Pifagor is succeeded by the Universe which has a starting point in time and neither beginning nor end in space. Merging of the STR and the NQM resulted in foundation of the quantum field the- ory, which constitutes the theoretical base of elementary particle physics. In the beginning it seemed that particle physics consisted of intuitive assumptions and set of recipes taken from ceiling. Each kind of fundamental interactions was studied separately, almost inde- pendently from other ones. The existence of divergences in the series of the perturbation theory was the only common trait, unifying all interactions. Only the theory of electromag- netic electron-positron interaction, the quantum electrodynamics, was a pleasant exception from such a dull landscape. The situation, however, changed abruptly by the beginning of the seventies in the XXth century. Velvet gauge revolution
Load more

Recommended publications
  • General Relativity and Cosmology: Unsolved Questions and Future Directions
    Article General Relativity and Cosmology: Unsolved Questions and Future Directions Ivan Debono 1,∗,† and George F. Smoot 1,2,3,† 1 Paris Centre for Cosmological Physics, APC, AstroParticule et Cosmologie, Université Paris Diderot, CNRS/IN2P3, CEA/lrfu, Observatoire de Paris, Sorbonne Paris Cité, 10, rue Alice Domon et Léonie Duquet, 75205 Paris CEDEX 13, France; [email protected] 2 Physics Department and Lawrence Berkeley National Laboratory, University of California, Berkeley, 94720 CA, USA 3 Helmut and Anna Pao Sohmen Professor-at-Large, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, 999077 Hong Kong, China * Correspondence: [email protected]; Tel.: +33-1-57276991 † These authors contributed equally to this work. Academic Editors: Lorenzo Iorio and Elias C. Vagenas Received: 21 August 2016; Accepted: 14 September 2016; Published: 28 September 2016 Abstract: For the last 100 years, General Relativity (GR) has taken over the gravitational theory mantle held by Newtonian Gravity for the previous 200 years. This article reviews the status of GR in terms of its self-consistency, completeness, and the evidence provided by observations, which have allowed GR to remain the champion of gravitational theories against several other classes of competing theories. We pay particular attention to the role of GR and gravity in cosmology, one of the areas in which one gravity dominates and new phenomena and effects challenge the orthodoxy. We also review other areas where there are likely conflicts pointing to the need to replace or revise GR to represent correctly observations and consistent theoretical framework. Observations have long been key both to the theoretical liveliness and viability of GR.
    [Show full text]
  • Conceptual Barriers to a Unified Theory of Physics 1 Introduction
    Conceptual barriers to a unified theory of physics Dennis Crossley∗ Dept. of Physics, University of Wisconsin-Sheboygan, Sheboygan, WI 53081 August 31, 2012 Abstract The twin pillars of twentieth-century physics, quantum theory and general relativity, have conceptual errors in their foundations, which are at the heart of the repeated failures to combine these into a single unified theory of physics. The problem with quantum theory is related to the use of the point-particle model, and the problem with general relativity follows from a misinterpretation of the significance of the equivalence principle. Correcting these conceptual errors leads to a new model of matter called the space wave model which is outlined here. The new perspective gained by space wave theory also makes it clear that there are conceptual errors in the two main thrusts of twenty-first- century theoretical physics, string theory and loop quantum gravity. The string model is no more satisfactory than the point-particle model and the notion that space must be quantized is, frankly, nonsensical. In this paper I examine all of these conceptual errors and suggest how to correct them so that we can once again make progress toward a unified theory of physics. 1 Introduction { the challenge of the unification program The goal of theoretical physics is to construct a single unified description of fundamental particles and their interactions, but flaws in the foundations of physics have prevented physi- cists from achieving this goal. In this essay I examine conceptual errors that have led to this impasse and propose alternatives which break this impasse and let us once again move forward toward the goal of a unified theory of physics.
    [Show full text]
  • (TEGR) As a Gauge Theory: Translation Or Cartan Connection? M Fontanini, E
    Teleparallel gravity (TEGR) as a gauge theory: Translation or Cartan connection? M Fontanini, E. Huguet, M. Le Delliou To cite this version: M Fontanini, E. Huguet, M. Le Delliou. Teleparallel gravity (TEGR) as a gauge theory: Transla- tion or Cartan connection?. Physical Review D, American Physical Society, 2019, 99, pp.064006. 10.1103/PhysRevD.99.064006. hal-01915045 HAL Id: hal-01915045 https://hal.archives-ouvertes.fr/hal-01915045 Submitted on 7 Nov 2018 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. Teleparallel gravity (TEGR) as a gauge theory: Translation or Cartan connection? M. Fontanini1, E. Huguet1, and M. Le Delliou2 1 - Universit´eParis Diderot-Paris 7, APC-Astroparticule et Cosmologie (UMR-CNRS 7164), Batiment Condorcet, 10 rue Alice Domon et L´eonieDuquet, F-75205 Paris Cedex 13, France.∗ and 2 - Institute of Theoretical Physics, Physics Department, Lanzhou University, No.222, South Tianshui Road, Lanzhou, Gansu 730000, P R China y (Dated: November 7, 2018) In this paper we question the status of TEGR, the Teleparallel Equivalent of General Relativity, as a gauge theory of translations. We observe that TEGR (in its usual translation-gauge view) does not seem to realize the generally admitted requirements for a gauge theory for some symmetry group G: namely it does not present a mathematical structure underlying the theory which relates to a principal G-bundle and the choice of a connection on it (the gauge field).
    [Show full text]
  • On the Goldstonic Gravitation Theory
    Pramina-J. Phys., Voi. 29, No. 1, July 1987, pp. 21-37. © Printed in India. On the Goldstonic gravitation theory D IVANENKO and G SARDANASHVILY Physics Faculty, Moscow University, 117234, Moscow, USSR Abstract. The physical specificity of gravity as a Goldstone-typ¢ field responsible for spontaneous breaking of space-time symmetries is investigated and extended up to supcrgrav- ity. Problems of the Higgs gravitation vacuum and its matter sources are discussed. A particular"dislocation" structure of a space-time due to Poincar6 translation gauge fields and the corresponding modification of Newton's gravitational potential are predicted. Keywords. Gauge theory; gravity; supergravity; Goldstone field. PACS Nos 04.50; 11.15 1. Introduction The geometric nature of gravity as a metric field was established by Einstein's general relativity which we take as the base of gravitation theory. The physical specificity of gravity as the Goldstone-type field is now clarified by means of gauge approach to gravitation theory (Sardanashvily 1980; Ivanenko and Sardanashvily 1983; Ivanenko et al 1985). At present, gauge theory is well known to provide the theoretical base of most part of current unification attempts in particle physics. Apparently, a necessary step for including gravity in the unified gauge picture of, fundamental interactions consists in constructing a comprehensive gauge gravitation theory itself. We share the opinion of many authors that a gauge gravitation theory must contain Einstein's general relativity as the particular case. However, the main dilemma that one faces is that Einstein's gravitational field is a metric (or tetrad) field, whereas gauge potentials are connections on fibre bundles.
    [Show full text]
  • Spacetime Geometric Structures and the Search for a Quantum Theory of Gravity
    Spacetime geometric structures and the search for a Quantum Theory of Gravity Mihaela Iftime Abstract. One of the biggest challenges to theoretical physics of our time is to ¯nd a background-independent quantum theory of gravity. Today one encounters a profusion of di®erent attempts at quantization, but no fully accepted - or acceptable, theory of quantum gravity. Any such approach requires a response to a question that lies at the heart of this problem. \How shall we resolve the tension between the background de- pendence of all hitherto-successful quantum theories, both non-relativistic quantum mechanics and special-relativistic quantum ¯eld theory, and the background independence of classical general relativity?" (see [28]) The need for a background-independent quantization procedure forms the starting point of my approach. In this paper I shall present a gauge-natural formulation of general relativity, and provide some insights into the struc- ture of the space of geometries, which plays an important role in the construction of a non-perturbative quantum gravity using a path integral approach, as well as in string theory (see e.g., [2, 18, 31]) M.S.C. 2000: 53-XX, 83-XX. Key words: Di®erential geometry, Relativity and gravitational theory. 1 Historical-Physical Motivation The most succesful among all gravitational theories is Einstein's theory of general relativity. In general relativity the ¯eld equations 1 are described in purely geometric terms: the space-time is a fairly smooth manifold M of dim n = 4 with a normal hyperbolic Riemannian structure { Lorentzian metric tensor g transforms at each point to the flat Minkowski metric ´ = diag(1; 1; 1; ¡1), and its timelike and null geodesics represent the paths of freely falling particles and light rays.
    [Show full text]
  • The Gauge Condition in Gravitation Theory with a Background Metric
    The gauge condition in gravitation theory with a background metric G. A. Sardanashvily Department of Theoretical Physics, Moscow State University, 117234 Moscow, Russia E-mail: [email protected] URL: http://webcenter.ru/∼sardan/ Abstract. In gravitation theory with a background metric, a gravitational field is described by a two-tensor field. The energy-momentum conservation law imposes a gauge condition on this field. Gravitation theory in the presence of a background metric remains under considera- tion. In particular, there are two variants of gauge gravitation theory [9, 10, 12]. The first of them leads to the metric-affine gravitation theory, while the second one (hence- forth BMT) deals with a background pseudo-Riemannian metric gµν and a non-degenerate µ (1,1)-tensor field q ν, regarded as a gravitational field. A Lagrangian of BMT is of the form LBMT = ǫLq + LAM + Lm, (1) µ where Lq is a Lagrangian of a tensor gravitational field q ν in the presence of a background µν µν metric g , LAM is a Lagrangian of the metric-affine theory where a metric g is replaced with an effective metric µν µ ν αβ g = q αq βg , (2) e and Lm is a matter field Lagrangian depending on an effective metric g and a general linear connection K (see, e.g., [5]). Note that, strictly speaking, g (2)e is not a metric, but there exists a metric whose coefficients equal gµν (2). Therefore,e one usually assumes that Lq depends on q only via an effective metriceg. arXiv:gr-qc/0301066v1 19 Jan 2003 A glance at the expression (1) shows that thee matter field equation in BMT is that of affine-metric theory where a metric g is replaced with an effective metric g.
    [Show full text]
  • Scalar Fields in Particle Physics
    UNIVERSIDADE DE LISBOA INSTITUTO SUPERIOR TÉCNICO Scalar Fields in Particle Physics Leonardo Antunes Pedro Supervisor: Doctor Gustavo da Fonseca Castelo Branco Thesis approved in public session to obtain the PhD Degree in Physics Jury final classification: Pass With Merit Jury Chairperson: Chairman of the IST Scientific Board Members of the Committee: arXiv:1608.01928v1 [hep-ph] 5 Aug 2016 Doctor Francisco José Botella Olcina Doctor Gustavo da Fonseca Castelo Branco Doctor Jorge Manuel Rodrigues Crispim Romão Doctor Maria Margarida Nesbitt Rebelo da Silva Doctor Paulo André de Paiva Parada Doctor David Emanuel da Costa 2015 UNIVERSIDADE DE LISBOA INSTITUTO SUPERIOR TÉCNICO Scalar Fields in Particle Physics Leonardo Antunes Pedro Supervisor: Doctor Gustavo da Fonseca Castelo Branco Thesis approved in public session to obtain the PhD Degree in Physics Jury final classification: Pass With Merit Jury Chairperson: Chairman of the IST Scientific Board Members of the Committee: Doctor Francisco José Botella Olcina, Full Professor, Instituto de Física Corpuscular, Universitat de València, Spain Doctor Gustavo da Fonseca Castelo Branco, Full Professor, Instituto Superior Técnico, Universidade de Lisboa Doctor Jorge Manuel Rodrigues Crispim Romão, Full Professor, Instituto Superior Técnico, Universidade de Lisboa Doctor Maria Margarida Nesbitt Rebelo da Silva, Principal Researcher, Instituto Superior Técnico, Universidade de Lisboa Doctor Paulo André de Paiva Parada, Assistant Professor, Faculdade de Ciências, Universidade da Beira Interior Doctor David Emanuel da Costa, Assistant Researcher, Instituto Superior Técnico, Universidade de Lisboa Funding Institutions Fundação para a Ciência e a Tecnologia 2015 | Campos escalares em Física de Partículas Leonardo Antunes Pedro Doutoramento em Física Orientador Doutor Gustavo da Fonseca Castelo Branco Resumo Alargar o sector escalar ajuda a estudar o mecanismo de Higgs e alguns problemas do Modelo Padrão.
    [Show full text]
  • General Relativity and Cosmology: Unsolved Questions and Future Directions
    Article General Relativity and Cosmology: Unsolved Questions and Future Directions Ivan Debono 1,∗,† and George F. Smoot 1,2,3,† 1 Paris Centre for Cosmological Physics, APC, AstroParticule et Cosmologie, Université Paris Diderot, CNRS/IN2P3, CEA/lrfu, Observatoire de Paris, Sorbonne Paris Cité, 10, rue Alice Domon et Léonie Duquet, 75205 Paris CEDEX 13, France 2 Physics Department and Lawrence Berkeley National Laboratory, University of California, Berkeley, 94720 CA, USA; [email protected] 3 Helmut and Anna Pao Sohmen Professor-at-Large, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, 999077 Hong Kong, China * Correspondence: [email protected]; Tel.: +33-1-57276991 † These authors contributed equally to this work. Academic Editors: Lorenzo Iorio and Elias C. Vagenas Received: 21 August 2016; Accepted: 14 September 2016; Published: 28 September 2016 Abstract: For the last 100 years, General Relativity (GR) has taken over the gravitational theory mantle held by Newtonian Gravity for the previous 200 years. This article reviews the status of GR in terms of its self-consistency, completeness, and the evidence provided by observations, which have allowed GR to remain the champion of gravitational theories against several other classes of competing theories. We pay particular attention to the role of GR and gravity in cosmology, one of the areas in which one gravity dominates and new phenomena and effects challenge the orthodoxy. We also review other areas where there are likely conflicts pointing to the need to replace or revise GR to represent correctly observations and consistent theoretical framework. Observations have long been key both to the theoretical liveliness and viability of GR.
    [Show full text]
  • Weak Space-Time Curvature Effects for Lepton Electric Charge Swap at High Energy Scale Elias Koorambas
    Weak Space-Time Curvature Effects for Lepton Electric Charge Swap at High Energy Scale Elias Koorambas To cite this version: Elias Koorambas. Weak Space-Time Curvature Effects for Lepton Electric Charge Swap atHigh Energy Scale. Journal of Magnetohydrodynamics, Plasma, and Space Research , NOVA SCIENCE PUBLISHERS, INC., 2015, 20 (3), pp.333-354. hal-01205635 HAL Id: hal-01205635 https://hal.archives-ouvertes.fr/hal-01205635 Submitted on 25 Sep 2015 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. Distributed under a Creative Commons Attribution - NonCommercial| 4.0 International License Chapter WEAK SPACE-TIME CURVATURE EFFECTS FOR LEPTON ELECTRIC CHARGE SWAP AT HIGH ENERGY SCALE E. Koorambas Ampelokipi, Athens, Greece ABSTRACT We investigate the nature of a new kind of space-time curvature effects, produced by electric charge swap (ECS) transformations between families of leptons in the six- dimensional space time, We find that lepton ECS-transformations form the proper + Lorentz group SO (1,3)(ECS). We show that Einstein-type theory of weak space-time ECS- curvature effects can be formulated from the SL(2,C)(ECS) gauge group by using ECS- tetrad formalism. The latter yields to massless electrically charged spin-2 (ECS-graviton), which mediates the ECS exchange interaction between families of leptons.
    [Show full text]
  • A Black Hole Solution of Higher-Dimensional Weyl-Yang
    A BLACK HOLE SOLUTION OF HIGHER-DIMENSIONAL WEYL YANG KALUZA KLEIN THEORY − − − Halil Kuyrukcu Physics Department, Zonguldak B¨ulent Ecevit University, Zonguldak, 67100, Turkey E-mail: [email protected] Abstract. We consider the Weyl Yang gauge theory of gravitation in a (4 + 3)- − dimensional curved space-time within the scenario of the non-Abelian Kaluza Klein − theory for the source and torsion-free limits. The explicit forms of the field equations containing a new spin current term and the energy-momentum tensors in the usual four dimensions are obtained through the well-known dimensional reduction procedure. In this limit, these field equations admit (anti-)dyon and magnetic (anti-)monopole solutions as well as non-Einsteinian solutions in the presence of a generalized Wu Yang − ansatz and some specific warping functions when the extra dimensions associated with the round and squashed three-sphere S3 are, respectively, included. The (anti- )dyonic solution has similar properties to those of the Reissner Nordstr¨om de Sitter − − black holes of the Einstein Yang Mills system. However, the cosmological constant − − naturally appears in this approach, and it associates with the constant warping function as well as the three-sphere radius. It is demonstrated that not only the squashing parameter ℓ behaves as the constant charge but also its sign can determine whether the solution is a dyon/monopole or an antidyon/antimonopole. It is also shown by using the power series method that the existence of nonconstant warping function is essential for finding new exact Schwarzschild-like solutions in the considered model. arXiv:1602.02418v2 [gr-qc] 23 Sep 2021 PACS numbers: 04.50.Cd, 04.50.Kd, 04.20.Jb, 04.70.Bw Keywords: Modified theories of gravity, kaluza-klein theories, exact solutions, classical black holes 1.
    [Show full text]
  • Gauge Gravitation Theory from the Geometric Viewpoint
    GAUGE GRAVITATION THEORY FROM THE GEOMETRIC VIEWPOINT G.SARDANASHVILY Department of Theoretical Physics, Moscow State University This is the Preface to the special issue of International Journal of Geometric Methods in Modern Physics 3, N.1 (2006) dedicated to the 50th anniversary of gauge gravitation theory. It addresses the geometry underlying gauge gravitation theories, their higher-dimensional, super- gauge, and non-commutative extensions. At present, Yang–Mills gauge theory provides a universal description of the fundamental electroweak and strong interactions. Gauge gravitation theory from the very beginning [1] aims to extend this description to gravity. It started with gauge models of the Lorentz, Poincar´egroups and general covariant transformations [2–4]. At present, gauge gravity is mainly supergravity, higher-dimensional, non-commutative and quantum gravity [5–8]. This Preface can not pretend for any comprehensive analysis of gauge gravitation theories, but addresses only the geometry underlying them. We apologize in advance for that the list of references is far from to be complete. The first gauge model of gravity was suggested by Utiyama [1] in 1956 just two years after birth of the gauge theory itself. Utiyama was first who generalized the original gauge model of Yang and Mills for SU(2) to an arbitrary symmetry Lie group and, in particular, to the Lorentz group in order to describe gravity. However, he met the problem of treating arXiv:gr-qc/0512115v2 9 Feb 2006 general covariant transformations and a pseudo-Riemannian metric (a tetrad field) which had no partner in Yang–Mills gauge theory. In a general setting, fiber bundles provide the adequate geometric formulation of classical field theory where classical fields on a smooth manifold X are represented by sections of fiber bundles over X.
    [Show full text]
  • Gauge Gravitation Theory. What Is the Geometry of the World?
    GAUGE GRAVITATION THEORY. WHAT IS GEOMETRY OF THE WORLD? Gennadi A Sardanashvily Department of Theoretical Physics, Physics Faculty, Moscow State University, 117234 Moscow, Russia E-mail: [email protected] When joined the unified gauge picture of fundamental interactions, the gravitation theory leads to geometry of a space-time which is far from simplicity of pseudo-Riemannian geometry of Einstein’s General Relativity. This is geometry of the affine-metric composite dislocated manifolds. The goal is modification of the familiar equations of a gravitational field and entirely the new equations of its deviations. In the present brief, we do not detail the mathematics, but discuss the reasons why it is just this geometry. The major physical underlying reason lies in spontaneous symmetry breaking when the fermion matter admits only the Lorentz subgroup of world symmetries of the geometric arena. I. Gauge theory is well-known to call into play the differential geometric methods in order to describe interaction of fields possessing a certain symmetry group. Moreover, it is this geometric approach phrased in terms of fibred manifolds which provides the adequate mathematical formulation of classical field theory. Note that the conventional gauge principle of gauge invariance of Lagrangian densities losts its validity since symmetries of realistic field models are almost always broken. We follow the geometric modification of the gauge principle which is formulated as follows. Classical fields can be identified with sections of fibred manifolds arXiv:gr-qc/9410045v1 30 Oct 1994 π : Y X (1) → whose n-dimensional base X is treated a parameter space, in particular, a world manifold.
    [Show full text]