DOCSLIB.ORG

A Covariant Canonical Quantization of General Relativity

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
A Covariant Canonical Quantization of General Relativity Hindawi Advances in High Energy Physics Volume 2018, Article ID 4537058, 7 pages https://doi.org/10.1155/2018/4537058 Research Article A Covariant Canonical Quantization of General Relativity Stuart Marongwe Department of Physics and Astronomy, Botswana International University of Science and Technology, P. Bag , Palapye, Botswana Correspondence should be addressed to Stuart Marongwe; [email protected] Received 13 June 2018; Accepted 8 November 2018; Published 19 December 2018 Guest Editor: Farook Rahaman Copyright © Stuart Marongwe. is is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. e publication of this article was funded by SCOAP. A Hamiltonian formulation of General Relativity within the context of the Nexus Paradigm of quantum gravity is presented. We show that the Ricci flow in a compact matter free manifold serves as the Hamiltonian density of the vacuum as well as a time evolution operator for the vacuum energy density. e metric tensor of GR is expressed in terms of the Bloch energy eigenstate functions of the quantum vacuum allowing an interpretation of GR in terms of the fundamental concepts of quantum mechanics. 1. Introduction the geometry and matter content of the universe of each time slice. However, the Hamiltonian no longer determines e gravitational field which is elegantly described by Ein- the evolution of the system and leads to the problem of stein’s field equations has so far eluded a quantum descrip- timelessness [, ]. Hawking rightly points out that the very tion.MuchefforthasbeenplacedintoformulatingGeneral act of splitting space-time into space and time destroys the Relativity (GR) in terms of Hamilton’s equations since a spirit of GR (general covariance) and therefore not much Hamiltonian formulation of a classical field theory leads can be gained from this approach to quantization of gravity. naturally to its quantization. e earliest such attempt is the Perturbative covariant approaches to the problem of quantum ADM formalism [], named for its authors Richard Arnowitt, gravity have an inherent weakness in that they depend on Stanley Deser, and Charles W. Misner first published in a fine classical background. It is therefore difficult to obtain . is formalism starts from the assumption that space a self-consistent quantum theory of gravity with a classical Σ is foliated into a family of time slices �,labeledbytheir background space-time. Steven Carlip [ , ] and Claus time coordinate t and with space coordinates on each slice � Kiefer [, ] have made excellent and extensive reviews of given by � . e dynamic variables of this theory are then the problems faced by current approaches to the problem taken to be the metric tensor of three-dimensional spatial of quantum gravity. Carlip [ ] in particular singles out the � �� � slices ��� (�.� ) andtheirconjugatemomenta� (�.� ).Using lack of a firm conceptual understanding of the foundational these variables it is possible to define a Hamiltonian and concepts of quantum gravity as the source of much of the thereby write the equations of motion for GR in Hamilton's difficulty in understanding quantum gravity. ese deep form.etimeslicesarethenweldedtogetherusingfour conceptual issues result in technical problems in the attempt Lagrange multipliers and components of a shi vector field. to develop a consistent quantum theory of gravity. An extensive review of this formalism can be found in the In this paper we report a successful covariant canonical literature notably in [– ]. quantization of the gravitational field which preserves the e ADM formalism was first applied by Bryce De Witt in success of GR while simultaneously explaining Dark Energy [] to quantize gravity which resulted in the Wheeler–De (DE) and Dark Matter (DM). is approach to quantization Witt equation of quantum gravity. It is a functional differen- takes place in -space of metric signature (-,,,) in which tial equation in which the three-dimensional spatial metrics the quanta are excitations of the quantum vacuum called havetheformofanoperatoractingonawavefunction. Nexus gravitons. ough the Nexus Paradigm has been is wave function contains all of the information about introduced in the following papers [– ], the aim of this Advances in High Energy Physics study is to explicitly express the Hamiltonian formulation where � is the amplitude of a displacement vector in of the theory using the Bloch eigenstate functions of the Minkowski space. If we consider the Hubble diameter as quantum vacuum. ese wave functions contain information the maximum dimension of the local patch of space then about the energy state of the quantum vacuum which in turn �=��� where ��� istheHubbleradius.ischoiceofa dictates the geometry of space-time. maximum amplitude is justified from the fact that we cannot physically interact with objects beyond the Hubble -radius. 2. Methods Itisimportanttonotethatthelineelementisthesquare of the amplitude of the displacement -vector. us if we Our first step towards a covariant canonical quantization are to express GR in terms of the language of QM we must begins with defining a quantized space-time and its quanta. make the radical assumption that the displacement vectors We then modify Einstein’s vacuum equations to be consistent in Minkowski space are pulses of -space which can be with the quantized space-time followed by the defining of expressed in terms of Fourier functions as follows: Hamilton’s equations of the quantized space-time. is step ∞ is then followed by the Poisson brackets which provide the � 2��� � ��� Δ�� = � ∫ sinc (��) � �� bridge between classical and quantum mechanics (QM). e �� −∞ ∞ ( ) covariant canonical quantization procedure is carried out � =� ∫ ����(���)�� within the context of the Nexus Paradigm of quantum gravity. −∞ 2� �=+∞ .. Quantization of -Space and the Nexus Graviton. e pri- �� = ∑ � Where �� �� () mary objective of physics is the study of functional relation- �=−∞ ships amongst measurable physical quantities. In particular, a unifying paradigm of physical phenomena should reveal ��� Here �(���) = sinc(��)� are Bloch energy eigenstate the functional relationship between the fundamental physical functions. e Bloch functions can only allow the four wave quantities of -space and -momentum. Currently GR and vector to assume the following quantized values: QM offer the best predictions of the results of measurement �� of physical phenomena in their respective domains using �� = �=±1,±2...1060 � () different languages. GR describes gravitation in the language ��� of geometry and thus far, it has been difficult to apply thethelanguageofwavefunctionsusedinQMtogive e minimum -radius in Minkowski space is the Planck - it a QM description. e problem of quantum gravity is length since it is impossible to measure this length without 60 therefore to interpret GR in terms of the wavefunctions of forming a black hole. e statesarisefromtheratioof QM.TranslatingthelanguageofmeasurementofGRintothat Hubble -radius to the Planck -length. e displacement - of QM becomes the primary objective of this present attempt vectors in each eigenstate of space-time generate an infinite to resolve the problem of quantum gravity. Bravais -lattice. Also, condition () transforms ( ) to Measurements in GR take place in a local patch of a ��1 Reimannian manifold. is local patch can be considered � � Δ�� =� ∫ ����(�,�,�)�� () asaflatMinkowskispace.elineelementinMinkowski −��1 space which is the subject of measurement can be computed through the inner product of the local coordinates as e second assumption we make is that each displacement - � 2 2 2 2 2 vector is associated with a conjugate pulse of four-momentum Δ� Δ�� =Δ� +Δ� +Δ� −� Δ� which can also be expressed as a Fourier integral =(�Δ�+�Δ�+�Δ�+���Δ�) () �� 2��1 1 ⋅ (�Δ� + �Δ� + �Δ� + ���Δ�) Δ�(�)� = �� ∫ �(�,�,�)�� � −�� 1 ( ) On multiplying the right hand side we see that to get all the ��1 cross terms such as Δ�Δ� to cancel out we must assume =�� ∫ ����(�,�,�)�� −��1 �� + �� = 0 () where �(1)� is the four-momentum of the ground state. �2 =�2 =⋅⋅⋅=1 A displacement -vector and its conjugate -momentum e above conditions therefore imply that the coefficients satisfy the Heisenberg uncertainty relation (�,�,�,�) generate a Clifford algebra and therefore must ℎ be matrices. We rewrite these coefficients in the -tuple Δ� Δ� ≥ () 1 2 3 0 � � 2 form as (� ,� ,� ,� ) which may be summarized using the Minkowski metric on space-time as follows: e Uncertainty Principle plays the important role of gener- � ] �] {� ,� }=2� () ating a vector bundle, out of the total uncertainty space E of trivial displacement -vectors from which a closed compact egammasareofcoursetheDiracmatrices.usinorder manifold X is formed, i.e., (� : � �→ �). Each point on the to satisfy () we can express a displacement -vector as manifold is associated with a vector which is along a normal � � Δ� =�� () to the manifold. Advances in High Energy Physics 2 2 −1 e wave packet described by () is essentially a particle of ��2 =−(1−( )) �2��2 +(1−( )) ��2 2 2 four-space. e spin of this particle can be determined from � � () 2 2 2 2 the fact that each component of the four-displacement vector +� (�� + sin ��� ) transforms according to the law ere are no singularities in (). At high energies, character- �� 1 � ized by microcosmic scale wavelengths of the Nexus graviton Δ� = exp ( ��� [��,��]) Δ� () � 8 � and high values of n,space-timeisflatandhighlycompact.
Load more

Recommended publications
  • 3+1 Formalism and Bases of Numerical Relativity
    3+1 Formalism and Bases of Numerical Relativity Lecture notes Eric´ Gourgoulhon Laboratoire Univers et Th´eories, UMR 8102 du C.N.R.S., Observatoire de Paris, Universit´eParis 7 arXiv:gr-qc/0703035v1 6 Mar 2007 F-92195 Meudon Cedex, France [email protected] 6 March 2007 2 Contents 1 Introduction 11 2 Geometry of hypersurfaces 15 2.1 Introduction.................................... 15 2.2 Frameworkandnotations . .... 15 2.2.1 Spacetimeandtensorfields . 15 2.2.2 Scalar products and metric duality . ...... 16 2.2.3 Curvaturetensor ............................... 18 2.3 Hypersurfaceembeddedinspacetime . ........ 19 2.3.1 Definition .................................... 19 2.3.2 Normalvector ................................. 21 2.3.3 Intrinsiccurvature . 22 2.3.4 Extrinsiccurvature. 23 2.3.5 Examples: surfaces embedded in the Euclidean space R3 .......... 24 2.4 Spacelikehypersurface . ...... 28 2.4.1 Theorthogonalprojector . 29 2.4.2 Relation between K and n ......................... 31 ∇ 2.4.3 Links between the and D connections. .. .. .. .. .. 32 ∇ 2.5 Gauss-Codazzirelations . ...... 34 2.5.1 Gaussrelation ................................. 34 2.5.2 Codazzirelation ............................... 36 3 Geometry of foliations 39 3.1 Introduction.................................... 39 3.2 Globally hyperbolic spacetimes and foliations . ............. 39 3.2.1 Globally hyperbolic spacetimes . ...... 39 3.2.2 Definition of a foliation . 40 3.3 Foliationkinematics .. .. .. .. .. .. .. .. ..... 41 3.3.1 Lapsefunction ................................. 41 3.3.2 Normal evolution vector . 42 3.3.3 Eulerianobservers ............................. 42 3.3.4 Gradients of n and m ............................. 44 3.3.5 Evolution of the 3-metric . 45 4 CONTENTS 3.3.6 Evolution of the orthogonal projector . ....... 46 3.4 Last part of the 3+1 decomposition of the Riemann tensor .
    [Show full text]
  • M-Theory Solutions and Intersecting D-Brane Systems
    M-Theory Solutions and Intersecting D-Brane Systems A Thesis Submitted to the College of Graduate Studies and Research in Partial Fulfillment of the Requirements for the degree of Doctor of Philosophy in the Department of Physics and Engineering Physics University of Saskatchewan Saskatoon By Rahim Oraji ©Rahim Oraji, December/2011. All rights reserved. Permission to Use In presenting this thesis in partial fulfilment of the requirements for a Postgrad- uate degree from the University of Saskatchewan, I agree that the Libraries of this University may make it freely available for inspection. I further agree that permission for copying of this thesis in any manner, in whole or in part, for scholarly purposes may be granted by the professor or professors who supervised my thesis work or, in their absence, by the Head of the Department or the Dean of the College in which my thesis work was done. It is understood that any copying or publication or use of this thesis or parts thereof for financial gain shall not be allowed without my written permission. It is also understood that due recognition shall be given to me and to the University of Saskatchewan in any scholarly use which may be made of any material in my thesis. Requests for permission to copy or to make other use of material in this thesis in whole or part should be addressed to: Head of the Department of Physics and Engineering Physics 116 Science Place University of Saskatchewan Saskatoon, Saskatchewan Canada S7N 5E2 i Abstract It is believed that fundamental M-theory in the low-energy limit can be described effectively by D=11 supergravity.
    [Show full text]
  • Richard Arnowitt, Bhaskar Dutta Texas A&M University Dark Matter And
    Dark Matter and Supersymmetry Models Richard Arnowitt, Bhaskar Dutta Texas A&M University 1 Outline . Understand dark matter in the context of particle physics models . Consider models with grand unification motivated by string theory . Check the cosmological connections of these well motivated models at direct, indirect detection and collider experiments 2 Dark Matter: Thermal Production of thermal non-relativistic DM: 1 Dark Matter content: ~ DM v m freeze out T ~ DM f 20 3 m/T 26 cm v 310 Y becomes constant for T>T s f 2 a ~O(10-2) with m ~ O(100) GeV Assuming : v ~ c c f 2 leads to the correct relic abundance m 3 Anatomy of sann Co-annihilation Process ~ 0 1 Griest, Seckel ’91 2 ΔM M~ M ~0 1 1 + ~ ΔM / kT f 1 e Arnowitt, Dutta, Santoso, Nucl.Phys. B606 (2001) 59, A near degeneracy occurs naturally for light stau in mSUGRA. 4 Models 5 mSUGRA Parameter space Focus point Resonance Narrow blue line is the dark matter allowed region Coannihilation Region 1.3 TeV squark bound from the LHC Arnowitt, Dutta, Santoso, Phys.Rev. D64 (2001) 113010 , Arnowitt, Dutta, Hu, Santoso, Phys.Lett. B505 (2001) 177 6 mSUGRA Parameter space Arnowitt, ICHEP’00, Arnowitt, Dutta, Santoso, Nucl.Phys. B606 (2001) 59, 7 Small DM at the LHC (or l+l-, t+t) High PT jet [mass difference is large] DM The pT of jets and leptons depend on the sparticle masses which are given by Colored particles are models produced and they decay finally to the weakly interacting stable particle DM R-parity conserving (or l+l-, t+t) High PT jet The signal : jets + leptons+ t’s +W’s+Z’s+H’s + missing ET 8 Small DM via cascade Typical decay chain and final states at the LHC g~ Jets + t’s+ missing energy ~ u uL Low energy taus characterize s the small mass gap e s s a However, one needs to measure M the model parameters to Y S predict the dark matter 0 u U ~ χ content in this scenario S 2 Arnowitt, Dutta, Kamon, Kolev, Toback 0 ~ ~ 1 Phys.Lett.
    [Show full text]
  • Roland E. Allen
    Roland E. Allen Department of Physics and Astronomy Texas A&M University College Station, Texas 77843-4242 [email protected] , http://people.physics.tamu.edu/allen/ Education: B.A., Physics, Rice University, 1963 Ph.D., Physics, University of Texas at Austin, 1968 Research: Theoretical Physics Positions: Research Associate, University of Texas at Austin, 1969 - 1970 Resident Associate, Argonne National Laboratory, summers of 1967 - 69 Assistant Professor of Physics, Texas A&M University, 1970 - 1976 Associate Professor of Physics, Texas A&M University, 1976 - 1983 Sabbatical Scientist, Solar Energy Research Institute, 1979 - 1980 Visiting Associate Professor of Physics, University of Illinois, 1980 - 1981 Professor of Physics, Texas A&M University, 1983 – Present Honors and Research Activities Honors Program Teacher/Scholar Award, 2005 University Teaching Award, 2004 College of Science Teaching Award, 2003 Deputy Editor, Physica Scripta (published for Royal Swedish Academy of Sciences), 2013-2016 Service on NSF, DOE, and university program evaluation panels, 1988-present Co-organizer of Richard Arnowitt Symposium (September 19-20, 2014) Organizer of Second Mitchell Symposium on Astronomy, Cosmology, and Fundamental Physics (April 10-14, 2006) Organizing Committee, Fifth Conference on Dark Matter in Astroparticle Physics (October 3-9, 2004) Organizer of Mitchell Symposium on Observational Cosmology (April 11-16, 2004) Organizer of Institute for Quantum Studies Research for Undergraduates Program (Summer, 2003) Organizer of Richard Arnowitt
    [Show full text]
  • Spacetime Penrose Inequality for Asymptotically Hyperbolic Spherical Symmetric Initial Data
    U.U.D.M. Project Report 2020:27 Spacetime Penrose Inequality For Asymptotically Hyperbolic Spherical Symmetric Initial Data Mingyi Hou Examensarbete i matematik, 30 hp Handledare: Anna Sakovich Examinator: Julian Külshammer Augusti 2020 Department of Mathematics Uppsala University Spacetime Penrose Inequality For Asymptotically Hyperbolic Spherically Symmetric Initial Data Mingyi Hou Abstract In 1973, R. Penrose conjectured that the total mass of a space-time containing black holes cannot be less than a certain function of the sum of the areas of the event horizons. In the language of differential geometry, this is a statement about an initial data set for the Einstein equations that contains apparent horizons. Roughly speaking, an initial data set for the Einstein equations is a mathematical object modelling a slice of a space-time and an apparent horizon is a certain generalization of a minimal surface. Two major breakthroughs concerning this conjecture were made in 2001 by Huisken and Ilmanen respectively Bray who proved the conjecture in the so-called asymptotically flat Riemannian case, that is when the slice of a space-time has no extrinsic curvature and its intrinsic geometry resembles that of Euclidean space. Ten years later, Bray and Khuri proposed an approach using the so-called generalized Jang equation which could potentially be employed to deal with the general asymptotically flat case by reducing it to the Riemannian case. Bray and Khuri have successfully implemented this strategy under the assumption that the initial data is spherically symmetric. In this thesis, we study a suitable modification of Bray and Khuri's approach in the case when the initial data is asymptotically hyperbolic (i.e.
    [Show full text]
  • Particles Meet Cosmology and Strings in Boston
    PASCOS 2004 Particles meet cosmology and strings in Boston PASCOS 2004 is the latest in the symposium series that brings together disciplines from the frontier areas of modern physics. Participants at PASCOS 2004 and the Pran Nath Fest, which were held at Northeastern University, Boston. They include Howard Baer - front row sixth from left - then, moving right, Alfred Bartl, Michael Dine, Bruno Zumino, Pran Nath, Steven Weinberg, Paul Frampton, Mariano Quiros, Richard Arnowitt, MaryKGaillard, Peter Nilles and Michael Vaughn (chair, local organizing committee). The Tenth International Symposium on Particles, Strings and Cos­ redshift surveys suggests that the critical matter density of the uni­ mology took place at Northeastern University, Boston, on 16-22 verse is Qm ~ 0.3, direct dynamical measurements combined with August 2004. Two days of the symposium, 18-19 August, were the estimates of the luminosity density indicate Qm = 0.1-0.2. She devoted to the Pran Nath Fest in celebration of the 65th birthday of suggested that the apparent discrepancy may result from variations Matthews University Distinguished Professor Pran Nath. The PASCOS in the dark-matter fraction with mass and scale. She also suggested symposium is the largest interdisciplinary gathering on the interface that gravitational lensing maps combined with large redshift sur­ of the three disciplines of cosmology, particle physics and string veys promise to measure the dark-matter distribution in the uni­ theory, which have become increasingly entwined in recent years. verse. The microwave background can also provide clues to inflation Topics at PASCOS 2004 included the large-scale structure of the in the early universe.
    [Show full text]
  • Republication Of: the Dynamics of General Relativity
    Gen Relativ Gravit (2008) 40:1997–2027 DOI 10.1007/s10714-008-0661-1 GOLDEN OLDIE Republication of: The dynamics of general relativity Richard Arnowitt · Stanley Deser · Charles W. Misner Published online: 8 August 2008 © Springer Science+Business Media, LLC 2008 Abstract This article—summarizing the authors’ then novel formulation of General Relativity—appeared as Chap. 7, pp. 227–264, in Gravitation: an introduction to current research, L. Witten, ed. (Wiley, New York, 1962), now long out of print. Intentionally unretouched, this republication as Golden Oldie is intended to provide contemporary accessibility to the flavor of the original ideas. Some typographical corrections have been made: footnote and page numbering have changed–but not section nor equation numbering, etc. Current institutional affiliations are encoded in: [email protected], [email protected], [email protected]. An editorial note to this paper and biographies of the authors can be found via doi:10.1007/s10714-008-0649-x. Original paper: R. Arnowitt, S. Deser and C. W. Misner, in Gravitation: an introduction to current research (Chap. 7). Edited by Louis Witten. John Wiley & Sons Inc., New York, London, 1962, pp. 227–265. Reprinted with the kind permissions of the editor, Louis Witten, and of all three authors. R. Arnowitt (B) Department of Physics, Texas A&M University, 4242 TAMU, College Station, TX 77843-4242, USA e-mail: [email protected] S. Deser (B) Mailstop 057, Brandeis University, 415 South Street, Waltham, MA 02454, USA e-mail: [email protected] Lauritsen Laboratory, California Institute of Technology, Pasadena, CA 91125, USA C. W.
    [Show full text]
  • Schwinger's Approach to Einstein's Gravity and Beyond
    Schwinger’s Approach to Einstein’s Gravity and Beyond∗ K. A. Milton Laboratoire Kastler Brossel, Universit´ePierre et Marie Curie, Campus Jussieu Case 74, F-75252 Paris Cedex 05, France† Julian Schwinger (1918–1994), founder of renormalized quantum electrodynamics, was arguably the leading theoretical physicist of the second half of the 20th century. Thus it is not surprising that he made contributions to gravity theory as well. His students made major impacts on the still uncompleted program of constructing a quantum theory of gravity. Schwinger himself had no doubt of the validity of general relativity, although he preferred a particle-physics viewpoint based on gravitons and the associated fields, and not the geometrical picture of curved spacetime. This note provides a brief summary of his contributions and attitudes toward the subject of gravity. PACS numbers: 04.20.Cv, 04.25,Nx, 04.60.Ds, 01.65.+g I. INTRODUCTION Julian Schwinger, founder, along with Richard Feynman and Sin-itiro Tomonaga, of renormalized Quantum Elec- trodynamics in 1947-48, was the first recipient (along with Kurt G¨odel) of the Einstein prize. (For biographical information about Schwinger see Refs. [1, 2].) He was always deeply appreciative of Einstein’s contributions to rel- ativity, quantum mechanics, and gravitation, and late in his career wrote a popularization of special and general relativity called Einstein’s Legacy [3], based on an Open University course. Thus it is surprising that at this late date, almost 20 years after Schwinger’s death, and nearly 60 after Einstein’s, to learn there was a scientific controversy between the two, as expressed through an AAS session entitled “Schwinger vs.
    [Show full text]
  • Program Friday, September 19, 2014* 9:00 A.M
    Symposium in Honor of Dr. Richard Arnowitt Texas A&M, College Station, Texas September 19-20, 2014 Program Friday, September 19, 2014* 9:00 a.m. – 9:25 a.m. Pastries and Coffee 9:25 a.m. – 9:30 a.m. Opening Remarks H. Joseph Newton, Dean, College of Science Chair: David M. Lee, Texas A&M University 9:30 a.m. – 10:15 a.m. A One‐World formulation of quantum mechanics Charles Misner, University of Maryland 10:15 a.m. – 11:00 a.m. Reminiscences of my work with Richard Arnowitt Pran Nath, Northeastern University 11:00 a.m. – 11:30 a.m. Break Chair: Wolfgang Schleich, Texas A&M and Ulm Universities 11:30 a.m. – 12:15 p.m. Yang‐Mills origin of gravitational symmetries Michael Duff, Imperial College London 12:15 p.m. – 1:30 p.m. Lunch Chair: Roy Glauber, Harvard and Texas A&M Universities 1:30 p.m. – 2:15 p.m. Quantum mechanics without state vectors Steven Weinberg, University of Texas at Austin 2:15 p.m. – 2:35 p.m. Travels with Julian: How Schwinger resolved a disagreement between Lamb and Wigner Marlan Scully, Texas A&M and Princeton Universities 2:35 p.m. – 3:00 p.m. Interconnection between particle physics and cosmology Bhaskar Dutta, Texas A&M University 3:00 p.m. – 3:30 p.m. Break Chair: Edward S. Fry, Texas A&M University 3:30 p.m. – 4:15p.m. The Legacy of ADM Stanley Deser, Brandeis and Caltech 4:30 p.m. – 4:30 p.m.
    [Show full text]
  • Constraints on the Minimal Supergravity Model from the B→Sγ Decay
    CTP-TAMU-03/94 NUB-TH.7316/94 CERN-TH.3092/94 March, 1994 Constraints on the minimal supergravity model from the b → sγ decay Jizhi Wu and Richard Arnowitt Department of Physics, Texas A&M University College Station, Texas 77843 and Pran Nath Theoretical Physics Division, CERN CH-1211 Geneva 23 and Department of Physics, Northeastern University Boston, Massachusetts 02115∗ Abstract The constraints on the minimal supergravity model from the b → sγ decay are stud- ied. A large domain in the parameter space for the model satisfies the CLEO bound, arXiv:hep-ph/9406346v1 21 Jun 1994 BR(b → sγ) < 5.4 × 10−4. However, the allowed domain is expected to diminish signifi- cantly with an improved bound on this decay. The dependence of the b → sγ branching ratio on various parameters is studied in detail. It is found that, for At < 0 and the top pole quark mass within the vicinity of the center of the CDF value, mt = 174±17 GeV, there exists only a small allowed domain because the light stop is tachyonic for most of the parameter space. A similar phenomenon exists for a lighter top and At negative when the GUT coupling constant is slightly reduced. For At > 0, however, the branching ratio is much less sensitive to small changes in mt, and αG. ∗ Permanent address PACS numbers: 12.10Dm, 11.30.Pb, 14.65.Fy, 14.40.Nd The extensive analyses of the high precision LEP data in the last few years have indicated that the idea of grand unification is only valid when combined with supersym- metry [1].
    [Show full text]
  • Curriculum Vitae Charles W
    Curriculum Vitae Charles W. Misner University of Maryland, College Park Education B.S., 1952, University of Notre Dame M.A., 1954, Princeton University Ph.D., 1957, Princeton University University Positions 1956{59 Instructor, Physics Department, Princeton University 1959{63 Assistant Professor, Physics, Princeton University 1963{66 Associate Professor, Department of Physics and Astronomy, University of Maryland 1966{2000 Professor, Physics, University of Maryland, College Park 1995{99 Assoc. Chair, Physics, University of Maryland 2000{ Professor Emeritus and Senior Research Scientist, Physics, University of Maryland Visitor 2005 (April, May) MPG-Alfred Einstein Institute, Postdam, Germany 2002 (January{March) MPG-Alfred Einstein Institute, Postdam, Germany 2000{01 (November{April) MPG-Alfred Einstein Institute, Postdam, Germany 2000 (January) Institute for Theoretical Physics, U. Cal. Santa Barbara 1983 (January) Cracow, Poland: Ponti¯cal Academy of Cracow 1980{81 Institute for Theoretical Physics, U. Cal. Santa Barbara 1977 (May) Center for Astrophysics, Cambridge, Mass. 1976 (June) D.A.M.T.P. and Caius College, Cambridge, U.K. 1973 (spring term) All Souls College, Oxford 1972 (fall term) California Institute of Technology 1971 (June) Inst. of Physical Problems, Academy of Sciences, USSR, Moscow 1969 (fall term) Visiting Professor, Princeton University 1976 (summer) Niels Bohr Institute, Copenhagen, Denmark 1966{67 Department of Applied Mathematics and Theoretical Physics, Cambridge University, England 1 1960 (spring term) Department of Physics, Brandeis University, Waltham, Massachusetts 1959 (spring and summer) Institute for Theoretical Physics, Copenhagen 1956 (spring and summer) Institute for Theoretical Physics, Leiden, the Netherlands Honors and Awards Elected Fellow of the American Academy of Arts & Sciences, May 2000 Dannie Heineman Prize for Mathematical Physics (Am.
    [Show full text]
  • Reminiscences of My Work with Richard Lewis Arnowitt
    Reminiscences of my work with Richard Lewis Arnowitt Pran Nath∗ Department of Physics, Northeastern University, Boston, MA 02115, USA This article contains reminiscences of the collaborative work that Richard Arnowitt and I did together which stretched over many years and encompasses several areas of particle theory. The article is an extended version of my talk at the Memorial Symposium in honor of Richard Arnowitt at Texas A&M, College Station, Texas, September 19-20, 2014. My collaboration with Richard Arnowitt (1928-2014)1 to constrain the parameters of the effective Lagrangian. started soon after I arrived at Northeastern University in The effective Lagrangian was a deduction from the fol- 1966 and continued for many years. In this brief article lowing set of conditions: (i) single particle saturation in on the reminiscences of my work with Dick I review some computation of T-products of currents, (ii) Lorentz in- of the more salient parts of our collaborative work which variance, (iii) “spectator” approximation, and (iv) local- includes effective Lagrangians, current algebra, scale in- ity which implies a smoothness assumption on the ver- variance and its breakdown, the U(1) problem, formu- tices. The above assumptions lead us to the conclusion lation of the first local supersymmetry and the develop- that the simplest way to achieve these constraints is via ment of supergravity grand unification in collaboration an effective Lagrangian which for T-products of three of Ali Chamseddine, and its applications to the search currents requires writing cubic interactions involving π,ρ for supersymmetry. and A1 fields and allowing for no derivatives in the first -order formalism and up to one-derivative in the second order formalism.
    [Show full text]