DOCSLIB.ORG

Introduction to Particle Physics I

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Introduction to Particle Physics I Introduction to Particle Physics Swedish Teacher program 2019 Lecture II 29/Oct/2019 G de Cataldo INFN Ba, It/CERN CH 1 EP-UAI Lecture II Introduction to the SM – The Standard Model – The Higgs mechanism in the SM (hints) – The detection of the Higgs boson The most part of figures and formulas are from A. Bettini, Introduction to elementary particle physics. II edition Cambridge U.P. 2016 29/Oct/2019 G de Cataldo INFN Ba, It/CERN CH 2 EP-UAI SM mathematical features • SM is based on: – Gauge Quantum Field Theory (QFT) that incorporates: • The Special Relativity (already introduced); • The Quantum Mechanics (already introduced); • Gauge invariance of the interactions (to be introduced!) • Rather complex mathematical framework mediated from the Quantum Electro Dynamics (QED) that successfully describe the electromagnetic interaction as gauge QFT ! 29/Oct/2019 G de Cataldo INFN Ba, It/CERN CH 3 EP-UAI Quantum Field Theory • Lamb and Retherford experiment in 1947 showed that the non-relativistic QM was not sufficient to describe the Nature!! • The result showed that the motion of the atomic electron could not be described simply by the Dirac equation in an external classical given field (that of the proton in this case); Virtual particle! Photon: the vector boson of the interaction 29/Oct/2019 G de Cataldo INFN Ba, It/CERN CH 4 EP-UAI QED Quantum Field Theory • In QFT , it is not only the photons that are quanta of a field but also the charged particles, like electrons and positrons are quanta of a field • Dirac equation is still valid but its interpretation changes: the 휓 becomes a mass field, the quantum field of electrons. 푒+푎푛푑 푒− are the source of the mass fields! • The fields are quantum operators to create and annihilate their quanta.(Feynman diagrams). Fundaments of the QED. 29/Oct/2019 G de Cataldo INFN Ba, It/CERN CH 5 EP-UAI Speaking of gauge invariance 29/Oct/2019 G de Cataldo INFN Ba, It/CERN CH 6 EP-UAI Gauge invariance in the EM field 1. There are forces (Coulomb) between stationary charges and additional forces (magnetic) between moving charges; 2. Electromagnetic radiation is emitted by accelerating charges and can be absorbed or scattered by bodies with electrical structure 3. Classical EM defines the fields E and B which obey Maxwell’s equations (1830, Unification of electrostatic and magnetism) DivE 0 DivB 0 B CurlE (2.1) t E CurlB 0(j 0 ) t • But this formulation is not invariant under Lorentz transform (L.I.) of space- time coordinates. 7/3/2018 Dep. of Physics, Giacinto de Cataldo INFN, Ba-It and 7 Malta CERN-CH [email protected] Gauge invariance in the EM field 1st step: 1st and 4th Maxwell equations (E,B) implies the conservation of the charge: 휕휌 (2.2) 휵 ∙ 푱 − = 0 휕푡 To express the Maxwell equations in a LI form, it is convenient to define the vector potential A and the (scalar) scalar potential 휑, such: B=퐶푢푟푙 푨 휕푨 E= - grad휑 - (2.3) 휕푡 The properties of A are such that the four-vector (A, 휑/c) transforms exactly as (r,ct) or the (p,E/c). So, the reformulation of the Maxwell equations using A and 휑 become L.I.! 7/3/2018 Dep. of Physics, Malta Giacinto de Cataldo INFN, Ba-It and CERN- 8 CH [email protected] Gauge invariance in the EM. field 2nd step In addition, the EM field shows a very important property, that of the gauge invariance. If A and 휑 are simultaneously changed in the following way: 휕χ 푨 → 푨′ = 푨 + 푟푎푑χ; 휑 → 휑′ = 휑 - 휕푡 (2.4) where 휒 is a scalar function of space and time 휒 = 휒(푥, 푦, 푧, 푡) (called gauge function), the observable fields E and B are unchanged! In fact replacing (2.4) in (2.3) , there is no change in E and B. B′ =푐푢푟푙푨′ = 푐푢푟푙(푨 + 푟푎푑휒) curlA = B) 휕푨′ 휕휒 휕(푨+품풓풂풅휒) 휕푨 E’= - grad휑’ - = −푟푎푑 휑 − − =− grad휑 − =E 휕푡 휕푡 휕푡 휕푡 The (2.4 ) is called gauge transformation. The EM theory is said gauge invariant or the EM has the gauge symmetry property. 7/3/2018 Dep. of Physics, Malta Giacinto de Cataldo INFN, Ba-It and CERN- 9 CH [email protected] Gauge invariance in QED • The theoretical motivations for charge conservation are extremely strong , since they are consequence of the gauge invariance of the theory; • Up to now we were speaking of the Relativistic Electrodynamics, NOT yet of gauge QFT. Now let’s start to describe it! • The scattering amplitude in QED is given by the matrix element of the interaction Hamiltonian: 푀푓푖 = 휓푓 퐻푄퐸퐷 휓푖 where 퐻푄퐸퐷= 퐻푄퐸퐷(푨푄푀 푓푖푒푙푑, 휑푄푀 푓푖푒푙푑) 7/3/2018 Dep. of Physics, Malta Giacinto de Cataldo INFN, Ba-It and CERN- 10 CH [email protected] Gauge invariance in QED • The gauge invariance of the QED Lagrangian (replacing the Hamiltonian) is ensured if the wave function of the charged particles is transformed at the same time as the quantum potential field 푨푄푀 푓푖푒푙푑, 휑푄푀 푓푖푒푙푑(V. Fock 1929) . • For an electron: 휓 ⟹ 휓′ = 푒푖휒(풓,푡) 휓 • 휓 is itself an operator of the field electrons that create and destroy the electron. The local gauge invariance of the Lagrangian implies the electric charge conservation, • the invariance held if the gauge boson, the photon in this case, is massless, as it is ! 7/3/2018 Dep. of Physics, Malta Giacinto de Cataldo INFN, Ba-It and CERN- 11 CH [email protected] Feynman diagrams for the QED fine structure constant is the EM coupling constant 훼 is NOT constant! depends on the E because of Scattering amplitude: the electric charge depends on E! Running constant Probability amplitude for the mediator The probability of this process, cross section, is proportional to the 2 2, 29/Oct/2019|1/m -t| the coupling constants, G de Cataldo INFN Ba, It/CERN CH 12 and to the phase space. EP-UAI Weak Interaction • WI are responsible of the decays in the radioactivity; • E. Fermi 1933 first theoretical description of B decay; • Matter and anti-mater behave differently w.r.t WI!! Reason of matter/anti-matter asymmetry in the Universe ?? • WI would be a gauge QFT if the vector bosons mediating the interaction are assumed massless! WARNING:W±, Z0 are massive!! • We need a mechanism providing mass to the W±, Z0 without destroying the gauge invariance! Higgs mechanism! 29/Oct/2019 G de Cataldo INFN Ba, It/CERN CH 13 EP-UAI Some Feynman diagrams of the WI Similarity with EM scattering! Z0 couples matter and antimatter partners fermion partners 29/Oct/2019 G de Cataldo INFN Ba, It/CERN CH 14 EP-UAI Quantum Chromo Dynamics (QCD) • Deep inelastic scattering with e on p and n demonstrate the existence of partons : finally the quarks; • Quarks interact strongly. They strong Gluon charges are named colors, Quark scattering with scattering with gluon exchange gluon exchange • Their values are: Red, Green Blue (RGB). Anti-colors exists. • 8 Gluons are the interaction mediators. They are massless. Differently from the photon, they are charged as well! • QCD is a “gauge QFT”. The strong charge is conserved! 29/Oct/2019 G de Cataldo INFN Ba, It/CERN CH 15 EP-UAI Origin of hadron masses and Quantum Vacuum 29/Oct/2019 G de Cataldo INFN Ba, It/CERN CH 16 EP-UAI Unification in the Standard Model • Space-time and local gauge symmetry are of fundamental importance in building the basic laws of the nature, the Standard Model; • EW unification started in 1960. From Fermi to gauge QFT: At that time, with a raw approximation, neglecting the quadri-momentum transfer, the MW could already be estimated: 2 2 4 2 퐺퐹 푀푊푐 퐺퐹 2 ≈ 2 4 푠표 푡ℎ푎푡 3 ≈ ℏ푐 푀푊푐 4휋 ℏ푐 4휋ℏ푐 2 2 푔 푒 1 2 If 푠 푡표 ℎ푎푣푒 푡ℎ푒 푠푎푚푒 푣푎푙푢푒 = 훼 = then 푀푊푐 ≈ 88 퐺푒푉! 4휋ℏ푐 4휋휀0ℏ푐 137 (83 the measured value!) 29/Oct/2019 G de Cataldo INFN Ba, It/CERN CH 17 EP-UAI Unification in the Standard Model • More formally: • The EW predict three gauge bosons and the relationship of their masses with two parameters: GF and 푠푒푛휃푊 with 휃푊 called “weak mixing angle. • The latter parameter imposes the photon to not couple with neutral current and the Z0 to be neutral. • 푠푒푛휃푊 can be measured only indirectly and it was done by UA1 and UA2 measuring the 푀푊 푎푛푑 푀푍0 (1983). 29/Oct/2019 G de Cataldo INFN Ba, It/CERN CH 18 EP-UAI 푈퐴1: 푀푀푤= 83 ± 3 퐺푒푉 0 − − 푍 → 푒 +푒 푈퐴1: 푀푍0= 93 ± 3 퐺푒푉 29/Oct/2019 G de Cataldo INFN Ba, It/CERN CH 19 EP-UAI And the interaction coupling constant constants? • The EM and Weak coupling constant are not independent but correlated by the EW theory. On the contrary , EW and DCD , both being gauge theories, are unified by the theoretical framework while their coupling constant are independent. • EW and QCD together form the SM of fundamental interactions . What about the evolution of their coupling constant? Comments in Beyond the SM! (lecture III) 29/Oct/2019 G de Cataldo INFN Ba, It/CERN CH 20 EP-UAI The Higgs mechanism • The Higgs mechanism was proposed (1960) to provide mass to the weak gauge bosons W± and Z°, the interaction carriers, without destroying the gauge invariance of the EW Lagrangian ! • this was to unify the Weak and EM interactions in a gauge QFT (Electroweak interaction); • After about 50 years, The Higgs boson has been observed at the LHC and presented on the 4th July 2012 at CERN; • The Higgs field fills the Universe with a non zero value and provides mass to the fundamental particles; 29/Oct/2019 G de Cataldo INFN Ba, It/CERN CH 21 EP-UAI Observation of the Higgs boson Two protons interacting in the LHC excite the Higgs field that manifests itself with the emission of the boson with a mass of 126 GeV.
Load more

Recommended publications
  • THE STRONG INTERACTION by J
    MISN-0-280 THE STRONG INTERACTION by J. R. Christman 1. Abstract . 1 2. Readings . 1 THE STRONG INTERACTION 3. Description a. General E®ects, Range, Lifetimes, Conserved Quantities . 1 b. Hadron Exchange: Exchanged Mass & Interaction Time . 1 s 0 c. Charge Exchange . 2 d L u 4. Hadron States a. Virtual Particles: Necessity, Examples . 3 - s u - S d e b. Open- and Closed-Channel States . 3 d n c. Comparison of Virtual and Real Decays . 4 d e 5. Resonance Particles L0 a. Particles as Resonances . .4 b. Overview of Resonance Particles . .5 - c. Resonance-Particle Symbols . 6 - _ e S p p- _ 6. Particle Names n T Y n e a. Baryon Names; , . 6 b. Meson Names; G-Parity, T , Y . 6 c. Evolution of Names . .7 d. The Berkeley Particle Data Group Hadron Tables . 7 7. Hadron Structure a. All Hadrons: Possible Exchange Particles . 8 b. The Excited State Hypothesis . 8 c. Quarks as Hadron Constituents . 8 Acknowledgments. .8 Project PHYSNET·Physics Bldg.·Michigan State University·East Lansing, MI 1 2 ID Sheet: MISN-0-280 THIS IS A DEVELOPMENTAL-STAGE PUBLICATION Title: The Strong Interaction OF PROJECT PHYSNET Author: J. R. Christman, Dept. of Physical Science, U. S. Coast Guard The goal of our project is to assist a network of educators and scientists in Academy, New London, CT transferring physics from one person to another. We support manuscript Version: 11/8/2001 Evaluation: Stage B1 processing and distribution, along with communication and information systems. We also work with employers to identify basic scienti¯c skills Length: 2 hr; 12 pages as well as physics topics that are needed in science and technology.
    [Show full text]
  • Charm Meson Molecules and the X(3872)
    Charm Meson Molecules and the X(3872) DISSERTATION Presented in Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy in the Graduate School of The Ohio State University By Masaoki Kusunoki, B.S. ***** The Ohio State University 2005 Dissertation Committee: Approved by Professor Eric Braaten, Adviser Professor Richard J. Furnstahl Adviser Professor Junko Shigemitsu Graduate Program in Professor Brian L. Winer Physics Abstract The recently discovered resonance X(3872) is interpreted as a loosely-bound S- wave charm meson molecule whose constituents are a superposition of the charm mesons D0D¯ ¤0 and D¤0D¯ 0. The unnaturally small binding energy of the molecule implies that it has some universal properties that depend only on its binding energy and its width. The existence of such a small energy scale motivates the separation of scales that leads to factorization formulas for production rates and decay rates of the X(3872). Factorization formulas are applied to predict that the line shape of the X(3872) differs significantly from that of a Breit-Wigner resonance and that there should be a peak in the invariant mass distribution for B ! D0D¯ ¤0K near the D0D¯ ¤0 threshold. An analysis of data by the Babar collaboration on B ! D(¤)D¯ (¤)K is used to predict that the decay B0 ! XK0 should be suppressed compared to B+ ! XK+. The differential decay rates of the X(3872) into J=Ã and light hadrons are also calculated up to multiplicative constants. If the X(3872) is indeed an S-wave charm meson molecule, it will provide a beautiful example of the predictive power of universality.
    [Show full text]
  • On the Possibility of Experimental Detection of Virtual Particles in Physical Vacuum Anatolii Pavlenko* Open International University of Human Development, Ukraine
    onm Pavlenko, J Environ Hazard 2018, 1:1 nvir en f E ta o l l H a a n z r a r u d o J Journal of Environmental Hazards ReviewResearch Article Article OpenOpen Access Access On the Possibility of Experimental Detection of Virtual Particles in Physical Vacuum Anatolii Pavlenko* Open International University of Human Development, Ukraine Abstract The article that you are about to read may surprise you because it looks at problems whose origin is little known and which are rarely taken into account. These problems are real and it is logical to think that the recent and large- scale multiplication of antennas and wind turbines with their earthing in pathogenic zones and the mobile telephony induce fields which modify the natural equilibrium of the soil and have effects on the biosphere. The development of new technologies, such as wind turbines or antennas, such as mobile telephony, induces new forms of pollution that spread through soil faults and can have a negative impact on the health of humans and animals. In the article we share our experience which led us to understand the link between some of these installations and the disorders observed in humans or animals. This is an attempt to change the presentation of the problem of protecting people from the negative impact of electronic technology in public opinion by explaining the reality of virtual particles and their impact on people. We are trying to widely discuss this propaganda about virtual particles. This is an attempt to deduce a discussion on the need to protect against the negative impact of electronic technology on the living in the realm of the radical.
    [Show full text]
  • Virtual Particle 1 Virtual Particle
    Virtual particle 1 Virtual particle In physics, a virtual particle is a transient fluctuation that exhibits many of the characteristics of an ordinary particle, but that exists for a limited time. The concept of virtual particles arises in perturbation theory of quantum field theory where interactions between ordinary particles are described in terms of exchanges of virtual particles. Any process involving virtual particles admits a schematic representation known as a Feynman diagram, in which virtual particles are represented by internal lines. [1][2] Virtual particles do not necessarily carry the same mass as the corresponding real particle, although they always conserve energy and momentum. The longer the virtual particle exists, the closer its characteristics come to those of ordinary particles. They are important in the physics of many processes, including particle scattering and Casimir forces. In quantum field theory, even classical forces — such as the electromagnetic repulsion or attraction between two charges — can be thought of as due to the exchange of many virtual photons between the charges. The term is somewhat loose and vaguely defined, in that it refers to the view that the world is made up of "real particles": it is not; rather, "real particles" are better understood to be excitations of the underlying quantum fields. Virtual particles are also excitations of the underlying fields, but are "temporary" in the sense that they appear in calculations of interactions, but never as asymptotic states or indices to the scattering matrix. As such the accuracy and use of virtual particles in calculations is firmly established, but their "reality" or existence is a question of philosophy rather than science.
    [Show full text]
  • Research Article Is the Free Vacuum Energy Infinite?
    Hindawi Publishing Corporation Advances in High Energy Physics Volume 2015, Article ID 278502, 3 pages http://dx.doi.org/10.1155/2015/278502 Research Article Is the Free Vacuum Energy Infinite? H. Razmi and S. M. Shirazi Department of Physics, The University of Qom, Qom 3716146611, Iran Correspondence should be addressed to H. Razmi; [email protected] Received 12 February 2015; Revised 14 April 2015; Accepted 16 April 2015 Academic Editor: Chao-Qiang Geng Copyright © 2015 H. Razmi and S. M. Shirazi. This 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. The publication of this article was funded by SCOAP3. Considering the fundamental cutoff applied by the uncertainty relations’ limit on virtual particles’ frequency in the quantum vacuum, it is shown that the vacuum energy density is proportional to the inverse of the fourth power of the dimensional distance of the space under consideration and thus the corresponding vacuum energy automatically regularized to zero value for an infinitely large free space. This can be used in regularizing a number of unwanted infinities that happen in the Casimir effect, the cosmological constant problem, and so on without using already known mathematical (not so reasonable) techniques and tricks. 1. Introduction 2. The Quantum Vacuum, Virtual Particles, and the Uncertainty Relations In the standard quantum field theory, not only does the vacuum (zero-point) energy have an absolute infinite value, The quantum vacuum is not really empty. It is filled with but also all the real excited states have such an irregular value; virtual particles which are in a continuous state of fluctuation.
    [Show full text]
  • Disappearance of Positronium Into Extra Dimensions
    Disappearance of positronium into extra dimensions Bachelor thesis (theoretical) physics Supervisor: Author: Prof. dr. R.G.E. Timmermans Guus Avis Second Corrector: S2563355 Dr. ir. C.J.G. Onderwater June, 2016 Abstract In this bachelor thesis, it is discussed whether the search for invisible decay of positronium could in the near future be used to test models with extra di- mensions. To this end, the energy spectrum and decay modes of positronium are discussed. An introduction to different models with extra dimensions is given and it is discussed how positronium could disappear due to the existence of extra dimensions. Limits from other processes on this disappearance rate are acquired and compared to experimental sensitivity which is realistic to obtain in the near future. It is concluded that it is very unlikely that this search for extra dimensions will be viable in the near future because there is too large a discrepancy between the limits and the aspired sensitivity. Contents 1 Structure of positronium 4 1.1 What is positronium? . 4 1.2 Central potential . 5 1.3 Wave functions . 7 2 Energy corrections 10 2.1 Perturbation theory . 10 2.2 Relativistic correction . 10 2.3 Spin-orbit interaction . 12 2.4 Spin-spin interaction . 15 2.5 Virtual annihilation . 18 2.6 Spectrum of positronium . 23 3 Decay of positronium 25 3.1 Transition probability . 25 3.2 Decay modes . 28 3.3 Lifetime . 30 4 Extra dimensions 33 4.1 Compactification and brane worlds . 33 4.2 Models with extra dimensions and their motivation . 34 4.2.1 Kaluza-Klein theory .
    [Show full text]
  • Beyond the Standard Model
    IASSNS-HEP-93/23 hep-ph/9304318 March 1993 ⋆ Beyond the Standard Model Frank Wilczek† School of Natural Sciences Institute for Advanced Study Olden Lane Princeton, N.J. 08540 ABSTRACT The standard model of particle physics is marvelously successful. However, it is obviously not a complete or final theory. I shall argue here that the structure of the standard model gives some quite concrete, compelling hints regarding what lies beyond. arXiv:hep-ph/9304318v1 30 Apr 1993 As befits a wise and efficient organizer, Bernard Sadoulet called to ask me to give this talk (with the assigned title) long in advance of the conference. Thus when I accepted his invitation it was with a certain sense of unreality. Only when the time came to prepare, did I realize what a difficult chore it was that I had taken on. For, first of all, there have been many many talks at previous conferences on the same subject (that is, with the same assigned title); and secondly, it is not a subject. The first factor makes it a challenge to say anything fresh; but fortunately the second permits considerable flexibility. ⋆ Invited talk at PASCOS Conference, Nov. 1992, Berkeley † Research supported in part by DOE grant DE-FG02-90ER40542. [email protected] What I decided to do, realizing that I would face a mixed audience including many astronomers and specialists in general relativity, was to try to convey in a simple but honest way the most compelling ideas I know that lead one to concrete expectations for physics beyond the standard model. And in judging what was compelling, I tried to put myself into the position of an intelligent and sympathetic but properly skeptical physicist from outside particle physics.
    [Show full text]
  • Paving Through the Vacuum 3 of the Fermion and Antifermion
    Draft to be submitted (will be inserted by the editor) Paving Through the Vacuum C.M.F. Hugon · V. Kulikovskiy the date of receipt and acceptance should be inserted later Abstract Using the model in which the vacuum is filled ΨΨ where Ψ defines the fermion field. Similarly, a tensor h i with virtual fermion pairs, we propose an effective descrip- field can only have a scalar expectation value. tion of photon propagationcompatible with the wave-particle All the virtual particles can exist only inside a Lorentz duality and the quantum field theory. space-time shell defined by the Heisenberg uncertainty prin- In this model the origin of the vacuum permittivity and ciple: ∆x∆p ~ and ∆E∆t ~ . The pairs are CP-symmetric, permeability appear naturally in the statistical description of ≥ 2 ≥ 2 which allow them to keep the total angular momentum,colour the gas of the virtual pairs. Assuming virtual gas in thermal and spin zero values. Considering the Pauli exclusion prin- equilibrium at temperature corresponding to the Higgs field ciple, the virtual fermions in different pairs with the same vacuum expectation value, kT 246.22GeV, the deduced ≈ type and spin cannot overlap, therefore the ensemble of vir- value of the vacuum magnetic permeability (magnetic con- tual particle pairs tends to expand, like a gas in an infinite stant) appears to be of the same order as the experimental vacuum. We expect that the virtual pair gas is in thermal value. One of the features that makes this model attractive equilibrium. The energy exchange between the virtual pairs is the expected fluctuation of the speed of light propagation can be possible due to, for example, the presence of the real that is at the level of σ 1.9asm 1/2.
    [Show full text]
  • Electron-Positron Annihilation and the New Particles
    Electron-Positron Annihilation and the New Particles Energetic collisions between electrons and positrons give rise to the unexpected particles discovered last November. They may help to elucidate the structure of more familiar particles by Sidney D. Drell hen matter and antimatter are few structureless entities that are truly of interactions they participate in, or, as Wbrought together, they can an­ fundamental. These constituent particles 'it is often put, according to the kinds of nihilate each other to form a have been named quarks. Different ver­ forces they "feel." The forces considered state of pure energy. A fundamental sions of the quark theory make different are the four fundamental ones that are principle of physics demands that the re­ predictions about what is to be expected believed to account for all observed in­ verse of that process also be possible: A in the aftermath of an electron-positron teractions of matter: gravitation, elec­ state of pure energy can (quite literally) annihilation, and it was hoped that the tromagnetism, the strong force and the materialize to form particles of ponder­ experiments would help to determine weak force. able mass. When the matter and anti­ which version is the correct one. In the everyday world gravitation is matter are an electron and a positron, As it turned out, the results of an ini­ the most obvious of the four forces; it the state formed by their annihilation tial series of experiments in 1973 and influences all matter, and the range over consists of electromagnetic energy. It is early 1974 were not in accord with any which it acts extends to infinity.
    [Show full text]
  • Virtual Particles
    Particle Physics Michaelmas Term 2009 Prof Mark Thomson g X g g X g Handout 3 : Interaction by Particle Exchange and QED Prof. M.A. Thomson Michaelmas 2009 100 Recap , Working towards a proper calculation of decay and scattering processes – e e– lnitially concentrate on: e+ • e+e– $ +– • e– q $ e– q – – e q q * In Handout 1 covered the relativistic calculation of particle decay rates and cross sections |M|2 x (phase space) flux * In Handout 2 covered relativistic treatment of spin-half particles Dirac Equation * This handout concentrate on the Lorentz Invariant Matrix Element • Interaction by particle exchange • Introduction to Feynman diagrams • The Feynman rules for QED Prof. M.A. Thomson Michaelmas 2009 101 Interaction by Particle Exchange • Calculate transition rates from Fermi’s Golden Rule where is perturbation expansion for the Transition Matrix Element •For particle scattering, the first two terms in the perturbation series can be viewed as: f f “ scattering in “scattering via an ” j a potential intermediate state” i i • “Classical picture”–particles act as sources for fields which give rise a potential in which other particles scatter – “action at a distance” • “Quantum Field Theory picture”–forces arise due to the exchange of virtual particles. No action at a distance + forces between particles now due to particles Prof. M.A. Thomson Michaelmas 2009 102 (start of non-examinable section) •Consider the particle interaction which occurs via an intermediate state corresponding to the exchange of particle •One possible space-time picture of this process is: a c Initial state i : Vji space Final state f : x Intermediate state j : V •This time-ordered diagram corresponds to bdfj a “emitting” x and then b absorbing x ijf time •The corresponding term in the perturbation expansion is: • refers to the time-ordering where a emits x before b absorbs it Prof.
    [Show full text]
  • The Uncertainty Principle, Virtual Particles and Real Forces
    SPECIAL FEATURE: TEACHING QUANTUM PHYSICS www.iop.org/journals/physed The uncertainty principle, virtual particles and real forces Goronwy Tudor Jones School of Education and School of Physics and Astronomy, University of Birmingham, Edgbaston, Birmingham B15 2TT, UK Abstract This article provides a simple practical introduction to wave–particle duality, including the energy–time version of the Heisenberg Uncertainty Principle. It has been successful in leading students to an intuitive appreciation of virtual particles and the role they play in describing the way ordinary particles, like electrons and protons, exert forces on each other. This resource article is based on experience of Classical physics input teaching this topic at an introductory level to a • Kinetic energy and momentum. It will variety of audiences. Several approaches have be assumed in this paper that the concepts been tried; this has been the most successful of kinetic energy E and momentum p have because the crucial argument—that the better the been discussed. (It takes typically a two- frequency of a wave is to be measured, the more hour session to get non-scientists to feel time is needed—is invariably produced by class comfortable with these ideas.) members, and seems intuitively reasonable to For the more mathematically inclined, it is them. worth pointing out that the three equations The material is divided into several sections: (1) Comments on preliminary ideas from classi- p2 E = 1 mv2 p = mv E = cal physics. 2 2m (2) A practical introduction to E = hf and p = h/λ (wave–particle duality). show that if we know any two of the quantities (3) The energy–time uncertainty relation as a E, p and v (speed) for an object, we can consequence of (2).
    [Show full text]
  • Arxiv:0904.2904V3 [Gr-Qc] 6 Oct 2010 Absit H Eut R Ie Xlctyfracsmrap Casimir a for Explicitly Hole
    Vacuum energy and the spacetime index of refraction: A new synthesis a,b M. Nouri-Zonoz ∗ a Department of Physics, University of Tehran, North Karegar Ave., Tehran 14395-547, Iran. b School of Astronomy and Astrophysics, Institute for Research in Fundamental Sciences (IPM), P. O. Box 19395-5531 Tehran, Iran. Abstract In 1 + 3 (threading) formulation of general relativity spacetime behaves analogous to a medium with a specific index of refraction with respect to the light propagation. Accepting the reality of zero-point energy, through the equivalence principle, we elevate this analogy to the case of virtual photon propagation in a quantum vacuum in a curved background spacetime. Employing this new idea one could examine the response of vacuum energy to the presence of a weak stationary gravitational field in its different quantum field theoretic manifestations such as Casimir effect and Lamb shift. The results are given explicitly for a Casimir apparatus in the weak field limit of a Kerr hole. arXiv:0904.2904v3 [gr-qc] 6 Oct 2010 ∗ Electronic address: [email protected] 1 I. INTRODUCTION There was a time that the concepts of vacuum, space and time were mostly thought to belong to the philosophical realm and it is amazing that they all mathematically formulated in the language of physics in the beginning of the last century through the introduction of quantum mechanics and relativity. Furthermore it seems that the most challenging endeavor of physicists, a quantum theory of gravity, could only be achieved through an appropriate conceptual unification of these fundamental concepts in a consistent mathematical setting.
    [Show full text]