Aalborg Universitet Photon-Graviton Interaction and CPH Theory Javadi
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Quantum Field Theory*
Quantum Field Theory y Frank Wilczek Institute for Advanced Study, School of Natural Science, Olden Lane, Princeton, NJ 08540 I discuss the general principles underlying quantum eld theory, and attempt to identify its most profound consequences. The deep est of these consequences result from the in nite number of degrees of freedom invoked to implement lo cality.Imention a few of its most striking successes, b oth achieved and prosp ective. Possible limitation s of quantum eld theory are viewed in the light of its history. I. SURVEY Quantum eld theory is the framework in which the regnant theories of the electroweak and strong interactions, which together form the Standard Mo del, are formulated. Quantum electro dynamics (QED), b esides providing a com- plete foundation for atomic physics and chemistry, has supp orted calculations of physical quantities with unparalleled precision. The exp erimentally measured value of the magnetic dip ole moment of the muon, 11 (g 2) = 233 184 600 (1680) 10 ; (1) exp: for example, should b e compared with the theoretical prediction 11 (g 2) = 233 183 478 (308) 10 : (2) theor: In quantum chromo dynamics (QCD) we cannot, for the forseeable future, aspire to to comparable accuracy.Yet QCD provides di erent, and at least equally impressive, evidence for the validity of the basic principles of quantum eld theory. Indeed, b ecause in QCD the interactions are stronger, QCD manifests a wider variety of phenomena characteristic of quantum eld theory. These include esp ecially running of the e ective coupling with distance or energy scale and the phenomenon of con nement. -
Gravitational Interaction to One Loop in Effective Quantum Gravity A
IT9700281 LABORATORI NAZIONALI Dl FRASCATI SIS - Pubblicazioni LNF-96/0S8 (P) ITHf 00 Z%i 31 ottobre 1996 gr-qc/9611018 Gravitational Interaction to one Loop in Effective Quantum Gravity A. Akhundov" S. Bellucci6 A. Shiekhcl "Universitat-Gesamthochschule Siegen, D-57076 Siegen, Germany, and Institute of Physics, Azerbaijan Academy of Sciences, pr. Azizbekova 33, AZ-370143 Baku, Azerbaijan 6INFN-Laboratori Nazionali di Frascati, P.O. Box 13, 00044 Frascati, Italy ^International Centre for Theoretical Physics, Strada Costiera 11, P.O. Box 586, 34014 Trieste, Italy Abstract We carry out the first step of a program conceived, in order to build a realistic model, having the particle spectrum of the standard model and renormalized masses, interaction terms and couplings, etc. which include the class of quantum gravity corrections, obtained by handling gravity as an effective theory. This provides an adequate picture at low energies, i.e. much less than the scale of strong gravity (the Planck mass). Hence our results are valid, irrespectively of any proposal for the full quantum gravity as a fundamental theory. We consider only non-analytic contributions to the one-loop scattering matrix elements, which provide the dominant quantum effect at long distance. These contributions are finite and independent from the finite value of the renormalization counter terms of the effective lagrangian. We calculate the interaction of two heavy scalar particles, i.e. close to rest, due to the effective quantum gravity to the one loop order and compare with similar results in the literature. PACS.: 04.60.+n Submitted to Physics Letters B 1 E-mail addresses: [email protected], bellucciQlnf.infn.it, [email protected] — 2 1 Introduction A longstanding puzzle in quantum physics is how to marry the description of gravity with the field theory of elementary particles. -
Multidisciplinary Design Project Engineering Dictionary Version 0.0.2
Multidisciplinary Design Project Engineering Dictionary Version 0.0.2 February 15, 2006 . DRAFT Cambridge-MIT Institute Multidisciplinary Design Project This Dictionary/Glossary of Engineering terms has been compiled to compliment the work developed as part of the Multi-disciplinary Design Project (MDP), which is a programme to develop teaching material and kits to aid the running of mechtronics projects in Universities and Schools. The project is being carried out with support from the Cambridge-MIT Institute undergraduate teaching programe. For more information about the project please visit the MDP website at http://www-mdp.eng.cam.ac.uk or contact Dr. Peter Long Prof. Alex Slocum Cambridge University Engineering Department Massachusetts Institute of Technology Trumpington Street, 77 Massachusetts Ave. Cambridge. Cambridge MA 02139-4307 CB2 1PZ. USA e-mail: [email protected] e-mail: [email protected] tel: +44 (0) 1223 332779 tel: +1 617 253 0012 For information about the CMI initiative please see Cambridge-MIT Institute website :- http://www.cambridge-mit.org CMI CMI, University of Cambridge Massachusetts Institute of Technology 10 Miller’s Yard, 77 Massachusetts Ave. Mill Lane, Cambridge MA 02139-4307 Cambridge. CB2 1RQ. USA tel: +44 (0) 1223 327207 tel. +1 617 253 7732 fax: +44 (0) 1223 765891 fax. +1 617 258 8539 . DRAFT 2 CMI-MDP Programme 1 Introduction This dictionary/glossary has not been developed as a definative work but as a useful reference book for engi- neering students to search when looking for the meaning of a word/phrase. It has been compiled from a number of existing glossaries together with a number of local additions. -
Geometric Justification of the Fundamental Interaction Fields For
S S symmetry Article Geometric Justification of the Fundamental Interaction Fields for the Classical Long-Range Forces Vesselin G. Gueorguiev 1,2,* and Andre Maeder 3 1 Institute for Advanced Physical Studies, Sofia 1784, Bulgaria 2 Ronin Institute for Independent Scholarship, 127 Haddon Pl., Montclair, NJ 07043, USA 3 Geneva Observatory, University of Geneva, Chemin des Maillettes 51, CH-1290 Sauverny, Switzerland; [email protected] * Correspondence: [email protected] Abstract: Based on the principle of reparametrization invariance, the general structure of physically relevant classical matter systems is illuminated within the Lagrangian framework. In a straight- forward way, the matter Lagrangian contains background interaction fields, such as a 1-form field analogous to the electromagnetic vector potential and symmetric tensor for gravity. The geometric justification of the interaction field Lagrangians for the electromagnetic and gravitational interactions are emphasized. The generalization to E-dimensional extended objects (p-branes) embedded in a bulk space M is also discussed within the light of some familiar examples. The concept of fictitious accelerations due to un-proper time parametrization is introduced, and its implications are discussed. The framework naturally suggests new classical interaction fields beyond electromagnetism and gravity. The simplest model with such fields is analyzed and its relevance to dark matter and dark energy phenomena on large/cosmological scales is inferred. Unusual pathological behavior in the Newtonian limit is suggested to be a precursor of quantum effects and of inflation-like processes at microscopic scales. Citation: Gueorguiev, V.G.; Maeder, A. Geometric Justification of Keywords: diffeomorphism invariant systems; reparametrization-invariant matter systems; matter the Fundamental Interaction Fields lagrangian; homogeneous singular lagrangians; relativistic particle; string theory; extended objects; for the Classical Long-Range Forces. -
Introduction to Gauge Theories and the Standard Model*
INTRODUCTION TO GAUGE THEORIES AND THE STANDARD MODEL* B. de Wit Institute for Theoretical Physics P.O.B. 80.006, 3508 TA Utrecht The Netherlands Contents The action Feynman rules Photons Annihilation of spinless particles by electromagnetic interaction Gauge theory of U(1) Current conservation Conserved charges Nonabelian gauge fields Gauge invariant Lagrangians for spin-0 and spin-g Helds 10. The gauge field Lagrangian 11. Spontaneously broken symmetry 12. The Brout—Englert-Higgs mechanism 13. Massive SU (2) gauge Helds 14. The prototype model for SU (2) ® U(1) electroweak interactions The purpose of these lectures is to give an introduction to gauge theories and the standard model. Much of this material has also been covered in previous Cem Academic Training courses. This time I intend to start from section 5 and develop the conceptual basis of gauge theories in order to enable the construction of generic models. Subsequently spontaneous symmetry breaking is discussed and its relevance is explained for the renormalizability of theories with massive vector fields. Then we discuss the derivation of the standard model and its most conspicuous features. When time permits we will address some of the more practical questions that arise in the evaluation of quantum corrections to particle scattering and decay reactions. That material is not covered by these notes. CERN Academic Training Programme — 23-27 October 1995 OCR Output 1. The action Field theories are usually defined in terms of a Lagrangian, or an action. The action, which has the dimension of Planck’s constant 7i, and the Lagrangian are well-known concepts in classical mechanics. -
3. Interacting Fields
3. Interacting Fields The free field theories that we’ve discussed so far are very special: we can determine their spectrum, but nothing interesting then happens. They have particle excitations, but these particles don’t interact with each other. Here we’ll start to examine more complicated theories that include interaction terms. These will take the form of higher order terms in the Lagrangian. We’ll start by asking what kind of small perturbations we can add to the theory. For example, consider the Lagrangian for a real scalar field, 1 1 λ = @ @µφ m2φ2 n φn (3.1) L 2 µ − 2 − n! n 3 X≥ The coefficients λn are called coupling constants. What restrictions do we have on λn to ensure that the additional terms are small perturbations? You might think that we need simply make “λ 1”. But this isn’t quite right. To see why this is the case, let’s n ⌧ do some dimensional analysis. Firstly, note that the action has dimensions of angular momentum or, equivalently, the same dimensions as ~.Sincewe’veset~ =1,using the convention described in the introduction, we have [S] = 0. With S = d4x ,and L [d4x]= 4, the Lagrangian density must therefore have − R [ ]=4 (3.2) L What does this mean for the Lagrangian (3.1)? Since [@µ]=1,wecanreado↵the mass dimensions of all the factors to find, [φ]=1 , [m]=1 , [λ ]=4 n (3.3) n − So now we see why we can’t simply say we need λ 1, because this statement only n ⌧ makes sense for dimensionless quantities. -
Gravity and Gauge Theory∗
Gravity and Gauge Theory∗ Steven Weinstein Department of Philosophy, Northwestern University Abstract Gauge theories are theories that are invariant under a characteristic group of “gauge” trans- formations. General relativity is invariant under transformations of the diffeomorphism group. This has prompted many philosophers and physicists to treat general relativity as a gauge theory, and diffeomorphisms as gauge transformations. I argue that this approach is misguided. The theories of three of the four fundamental interactions of nature are “gauge” theories. A central feature of such theories is their invariance under a group of local transformations, i.e., transformations which may vary from spacetime point to spacetime point. The characteristic group of these “gauge” transformations is called the “gauge group.” The theory of the fourth interaction, gravity, is general relativity. General relativity has its own invariance group, the diffeomorphism group. Insofar as one understands “gauge theory” to mean a theory in which “the physics” (more on the ambiguity of this term later) is invariant under a certain group of transformations, one might be tempted to construe general relativity as a gauge theory.1 Just such a construal Þgures in recent work of Belot (1996) and Belot & Earman (1999a,b), who follow many (but not all) physicists in treating the diffeomorphism group as a gauge group, and who draw implications for the “hole argument.”2 In this paper, I show that general relativity is not a gauge theory at all, in the speciÞc sense that “gauge theory” has in elementary particle physics. This issue is of crucial importance to attempts to quantize general relativity, because in quantum theory, the generators of gauge transformations are emphatically not treated as observables, while the generators of spatiotemporal (e.g., Lorentz) transformations are in fact the canonical observables. -
The Strong Interactions*
SLAC-PUB-7239 July 1996 The Strong Interactions* R ICHARD B LANKENBECLER AND S TANLEY J. BRODSKY Stanford Linear Accelerator Center Stanford University, Stanford, California 94309 Article for the Encyclopedia of Applied Physics. * Work supported by the Department of Energy, contract DE–AC03–76SF00515. Abstract Physicists have traditionally classified the forces of nature into four categories: the strong interactions— the short-range forces which describe the interactions be- tween hadrons, such as the nucleon and pion and which bind protons and neutrons into atomic nuclei; the electromagnetic interactions— which bind electrons and nu- clei into atomic and molecular systems; the weak interactions— which cause the radioactive decay of nuclei; and the gravitational interactions— which are manifest in the motion of macroscopic objects such as planets. By definition, all parti- cles which interact strongly are called hadrons. In the period immediately after 1967, a remarkable scientific revolution occurred in which it was found that the strong interactions between hadrons could be described in terms of fundamental quark and gluon degrees of freedom which also provided a simple “periodic table” classifying the number and types of observed hadrons. The mathematical theory describing the interactions of the basic constituents of matter is called quantum chromodynamics, a theory in which quarks and gluons are permanently confined by increasingly strong forces at large distance. Conversely, QCD possesses the property of “asymptotic freedom”; that is, the effective strength of the fundamen- tal forces vanishes as the distance scale goes to zero. This is the reason that high energy inelastic large momentum transfer electron-proton scattering can be rather accurately viewed as scattering from quarks that act as though they were free but are permanently confined. -
Systems Engineering and System Definitions
® Systems Engineering and System Definitions Version: 1.0 Issued on: 8 January 2019 AUTHOR TEAM Hillary Sillitto, James Martin, Dorothy McKinney, Regina Griego, Dov Dori, Daniel Krob, Patrick Godfrey, Eileen Arnold, Scott Jackson 2 COPYRIGHT INFORMATION This INCOSE Technical Product was prepared by the International Council on Systems Engineering (INCOSE). It is approved by the INCOSE Technical Operations Leadership for release as an INCOSE Technical Product. Copyright (c) 2019 by INCOSE, published under Open Access. Systems Engineering and System Definitions INCOSE-TP-| 22 July 2019 ® 3 EXECUTIVE SUMMARY The Fellows Initiative on System and Systems Engineering Definitions was established in 2016, to: 1. review current INCOSE definitions of SYSTEM and SYSTEMS ENGINEERING; and 2. recommend any changes necessary to align the definitions to current practice and to the aspirations of INCOSE’s 2025 Vision. This document presents the final proposals from the initiative. It takes into account the extensive comments received during the review of the previous draft in September 2018. The review was open to all INCOSE members, and attracted over 350 individual comments and suggestions. The three key recommendations – for definitions of systems engineering, engineered system, and a general definition of system - are presented below, with a very brief contextual explanation. After the table of contents, the main body of this document provides more explanation of these definitions, and also defines other specific system types and categories that are important for the systems engineering community. Systems Engineering is a transdisciplinary and integrative approach to enable the successful realization, use, and retirement of engineered systems, using systems principles and concepts, and scientific, technological, and management methods. -
Computational Chemistry of Non-Covalent Interaction and Its Application in Chemical Catalysis
Utah State University DigitalCommons@USU All Graduate Theses and Dissertations Graduate Studies 5-2016 Computational Chemistry of Non-Covalent Interaction and its Application in Chemical Catalysis Vincent de Paul Nzuwah Nziko Utah State University Follow this and additional works at: https://digitalcommons.usu.edu/etd Part of the Chemistry Commons Recommended Citation Nziko, Vincent de Paul Nzuwah, "Computational Chemistry of Non-Covalent Interaction and its Application in Chemical Catalysis" (2016). All Graduate Theses and Dissertations. 5248. https://digitalcommons.usu.edu/etd/5248 This Dissertation is brought to you for free and open access by the Graduate Studies at DigitalCommons@USU. It has been accepted for inclusion in All Graduate Theses and Dissertations by an authorized administrator of DigitalCommons@USU. For more information, please contact [email protected]. COMPUTATIONAL CHEMISTRY OF NON-COVALENT INTERACTION AND ITS APPLICATION IN CHEMICAL CATALYSIS by Vincent de Paul Nzuwah Nziko A dissertation submitted in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY in Chemistry Approved: Steve Scheiner Alexander I. Boldyrev Major Professor Committee Member Alvan Hengge T.C. Shen Committee Member Committee Member Cheng-Wei Tom Chang Mark R. McLellan Committee Member Vice President for Research and Dean of the School of Graduate Studies UTAH STATE UNIVERSITY Logan, Utah 2016 ii Copyright © Vincent de Paul Nzuwah Nziko 2016 All Rights Reserved iii ABSTRACT Computational Chemistry of Non-Covalent Interaction and its Application in Chemical Catalysis by Vincent de Paul Nzuwah Nziko, Doctor of Philosophy Utah State University, 2016 Major Professor: Dr. Steve Scheiner Department: Chemistry and Biochemistry Unconventional non-covalent interactions such as halogen, chalcogen, and tetrel bonds are gaining interest in several domains including but not limited to drug design, as well as novel catalyst design. -
Interaction of Elementary Particles from the Point of View of Nonlinear
1 Interaction description from the non-linear electromagnetic theory point of view Alexander G. Kyriakos Saint-Petersburg State Institute of Technology, St. Petersburg, Russia. Present address: Athens, Greece, e-mail: [email protected] Abstract In previous papers we have shown, that there is a special kind of non-linear electrodynamics (which we name Curvilinear Wave Electrodynamics - CWED), whose equations are mathematically equivalent to the equations of photons and leptons of quantum electrodynamics. The purpose of the present paper is to show that in framework of CWED the description of the interaction is also mathematically equivalent to description of the interaction in quantum physics. Another purpose of this paper is to show, that CWED allows to unify the description of interactions in physics. Keywords: non-linear field theory, classical electrodynamics, quantum electrodynamics 1.0. Introduction. A modern state of the interaction description. In previous papers [1,2] we have shown, that there is a non-linear electrodynamics - the curvilinear waves electrodynamics (CWED), whose equations are mathematically equivalent to the equations of quantum electrodynamics. The purpose of present paper is to show, that the mathematical description of interaction in CWED are also equivalent to that both in classical and quantum mechanics. It is known that interaction defines the most important characteristics of the matter motion and in form of the force or energy it is included in all equations of motion: equations of Newton, Schroedinger, Dirac, equations of weak and strong interactions, etc. 1.1. Force and energy forms of the interaction description As it is known, interaction can be expressed as force and as energy. -
The Fate of 'Particles' in Quantum Field Theories with Interactions 1 Introduction
The fate of ‘particles’ in quantum field theories with interactions Doreen Fraser Dept. of Philosophy University of Waterloo [email protected] ABSTRACT: Most philosophical discussion of the particle concept that is afforded by quantum field theory has focused on free systems. This paper is devoted to a systematic investigation of whether the particle concept for free systems can be extended to interacting systems. The possible methods of accomplishing this are considered and all are found unsatisfactory. Therefore, an interacting system cannot be interpreted in terms of particles. As a consequence, quantum field theory does not support the inclusion of particles in our ontology. In contrast to much of the recent discussion on the particle concept derived from quantum field theory, this argument does not rely on the assumption that a particulate entity be localizable. KEYWORDS: quantum field theory, quanta, particle, interaction 1Introduction Quantum field theory (QFT) is the basis of the branch of physics known as “particle physics.” However, the philosophical question of whether quantum field theories genuinely describe parti- cles is not straightforward to answer. Since QFT’s are formulated in terms of fields (i.e., mathe- matical expressions that associate quantities with points of spacetime), the issue is whether the formalism can be interpreted in terms of a particle notion. What is at stake is whether QFT, one of our current best physical theories, supports the inclusion of particles in our ontology. This 1 paper advances an argument that, because systems which interact cannot be given a particle interpretation, QFT does not describe particles. Even proponents of a particle interpretation of QFT acknowledge that the particle concept inherent in a QFT would differ from the classical particle concept in many ways.