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A Grand Tour of Physics Particle Physics A GRAND TOUR OF PHYSICS PARTICLE PHYSICS LECTURE 4 APR. 12, 2019 DR. GEORGE DERISE 1:30 – 3:30 PROFESSOR EMERITUS, MATHEMATICS TNCC THOMAS NELSON COMMUNITY ROOM 328. COLLEGE SPRING 2019 The Particle Zoo R,G,B QED, THE STRANGE THEORY OF LIGHT AND MATTER RICHARD FEYNMAN QUANTUM ELECTRODYNAMICS (QED) QUANTUM FIELD THEORY OF THE ELECTROMAGNETIC FORCE QUANTUM CHROMODYNAMICS (QCD) QUANTUM FIELD THEORY OF THE STRONG NUCLEAR FORCE. QUANTUM FLAVORDYNAMICS (QFD) (?) QUANTUM FIELD THEORY OF THE ELECTROWEAK FORCE. FIELD THEORY QUANTUM ELECTRODYNAMICS; FEYNMAN DIAGRAMS SOLID LINES - ELECTRONS (WAVEFUNCTIONS)- MATTER PARTICLES; FERMIONS WAVY (OR DASHED) LINE - PHOTON - FORCE PARTICLE; BOSON COUPLING CONSTANT STRENGTH α= 1/137 INFINITE SERIES EXPANSIONS The infinite series S converges to 2. S=2. The infinite series above diverges to ∞ 1 1 1 푀 = 1 + + + +. 102 104 106 FEYNMAN DIAGRAMS REPRESENTING A SERIES OF MATHEMATICAL CALCULATIONS A PERTURBATION SERIES The term proportional to alpha cubed requires 72 diagrams. The term proportional to alpha to the fourth requires 891diagrams. (actually only 86 integrals But they’re 10 dimensional EACH having about 20,000 terms!!) Right now progress is being made on the 12672 diagrams involving the fifth power! QED THE STRANGE THEORY OF LIGHT AND MATTER Richard Feynman Dirac's number (experiment) 1.00115965221 Dirac’s number (theory) 1.00115965246 SYMMETRY IN NATURE, PHYSICS AND MATH MATHEMATICAL GROUPS Z = . −ퟑ, −ퟐ, −ퟏ, ퟎ, +ퟏ, +ퟐ, +ퟑ. A GROUP… • IT’S A SET OF OBJECTS • YOU CAN COMBINE ANY TWO OBJECTS TO GET A THIRD OBJECT IN THE SET. • THERE IS A ‘NEUTRAL’ OBJECT. • FOR EVERY OBJECT THERE IS AN OPPOSITE THAT GETS YOU BACK TO ‘NEUTRAL’ THE SET OF INTEGERS FORMS A GROUP WITH RESPECT TO ADDITION SYMMETRIES OF THE EQUILATERAL TRIANGLE A HYPOTHETICAL WORLD e-, μ-, τ- THREE LEPTONS- ELECTRON, MUON, TAU (ASSUME THEY HAVE THE SAME MASS) IF MUON, μ- REPLACED THE ELECTRON e- IN AN ATOM PHYSICS WOULD BE THE SAME. A SYMMETRY OF NATURE THIS HYPOTHETICAL WORLD IS INVARIANT UNDER THE INTERCHANGE OF ELECTRONS, MUONS, AND TAUS. GROUP THEORY-THE ALGEBRA OF SYMMETRY ROTATIONS IN 3 SPACE ARE NON COMMUTATIVE, I.E. NON ABELIAN (R1)(R2) ≠ (R2)(R1) NOETHER’S THEOREM: CONSERVATION LAWS FOLLOW FROM THE SYMMETRY PROPERTIES OF NATURE. IF A SYSTEM HAS A CONTINUOUS SYMMETRY, THEN THERE ARE CORRESPONDING QUANTITIES WHOSE VALUES ARE CONSERVED IN TIME. SPACETIME SYMMETRIES INDEPENDENCE OF TIME → ENERGY CONSERVATION. INDEPENDENCE OF POSITION → MOMENTUM CONSERVATION. INDEPENDENCE OF DIRECTION → ANGULAR MOMENTUM CONSERVATION. ? → CHARGE CONSERVATION SPACETIME GROUPS 3+3+1+3=10 EACH A SUBGROUP OF THE 10 DIMENSIONAL POINCARÉ GROUP ALGEBRA OF MINKOWSKI SPACETIME- SPECIAL RELATIVITY WHAT IS THE SYMMETRY THAT IMPLIES CHARGE CONSERVATION ? MATH PHYSICS Given, a length L at A Given, a wave function ѱ(x). Apply a rigid body transformation T Shift the phase of ѱ in the Lagrangian L Length L before at A Lagrangian L before Equals the length L after at B equals the Lagrangian L after Implies This implies Conservation of distance Conservation of Electric Charge (Euclidean Geometry) (Electrodynamics) INTERNAL SYMMETRY LIE GROUP (CONTINUOUS GROUP) THE LAGRANGIAN L ( an expression involving energy) IS THE THEORY. Recall: The Action involves the LAGRANGIAN L. FROM L WE CAN DERIVE THE EQUATION(S) OF THE THEORY. THE WAVE FUNCTION IS THE SOLUTION OF SCHRÖDINGER’S EQUATION. THE WAVE FUNCTION HAS AN AMPLITUDE AND A PHASE. PHASE: ITS VALUE DOES NOT TELL ANYTHING ABOUT THE MAGNITUDES OR DIRECTIONS OF MEASURABLE OBSERVABLES. A SHIFT IN THE PHASE OF THE ELECTRON WAVE FUNCTION OF ANY ANGLE HAS NO PHYSICAL CONSEQUENCE. (GLOBAL PHASE INVARIANCE). THE LAGRANGIAN L OF THE ELECTRON WAVE FUNCTION IS INVARIANT WITH RESPECT TO A CERTAIN SYMMETRY (GROUP) TRANSFORMATION. A GLOBAL SYMMETRY: If we move the A LOCAL GAUGE SYMMETRY, however, is one point on the circle by the same where we can do an independent rotation amount everywhere in space, at each point in space then the laws of physics (i.e. A LOCAL TRANSFORMATION): should be the same: If a symmetry is a gauge symmetry, then this Conserved quantity electric charge transformation should still leave the laws of physics the same. U(1) (a) 2 slit experiment; electron field forms an interference pattern. (b) Shifting the phase of the entire field by the same amount (global) leaves the interference pattern unchanged. (Invariance under a global transformation) (c) Shifting the phase of a part of the field (local) changed the interference pattern. (d) A solenoid is placed where the electron field intensity is almost zero. A current in the solenoid created a magnetic field inside the solenoid and an electric potential outside. As the current varies the value of the electric potential changes and the original pattern is restored. A LOCAL GAUGE SYMMETRY: We can do an independent rotation at each point in space. BASICS OF GAUGE THEORY FOR QED: TO HAVE CONSERVATION OF ELECTRIC CHARGE THE LAGRANGIAN L WHICH DESCRIBES THE ELECTRON WAVE FUNCTION MUST BE INVARIANT UNDER SHIFT IN THE WAVE FUNCTION BY THE GROUP U(1). IF WE DO A LOCAL TRANSFORMATION, THE NEW LAGRANGIAN L* IS NOT EQUAL TO THE ORIGINAL L. THE THEORY IS NO LONGER INVARIANT. INTRODUCE ANOTHER FIELD WHICH COMPENSATES FOR THIS CHANGE. THIS IS THE ELECTROMAGNETIC FIELD. INVARIANCE OF L UNDER LOCAL GAUGE TRANSFORMATION REQUIRES THE EXISTENCE OF THE PHOTON Theory of the electron- Dirac’s Equation prediction of the existence of anti-matter 흍electron = 흍ퟏ + 풊흍ퟐ ퟐ 흍positron = 흍ퟏ − 풊흍ퟐ ퟐ http://www.slimy.com/~steuard/research/StringIntro/slide14.html Hydrogen atom- electron and proton Antihydrogen atom- positron and antiproton. PAULI EXCLUSION PRINCIPLE : FERMI-DIRAC STATISTICS FERMI–DIRAC STATISTICS apply to particles with half-integer spin-FERMIONS. It describe a distribution of particles over energy states in systems consisting of many identical particles that obey the PAULI EXCLUSION PRINCIPLE. THE PAULI EXCLUSION PRINCIPLE states that two or more identical fermions (particles with half-integer spin) cannot occupy the same quantum state within a quantum system simultaneously. BOSE–EINSTEIN STATISTICS Particles with an integer spin – BOSONS are not subject to the Pauli exclusion principle: any number of identical bosons can occupy the same quantum state. ISOSPIN: A symmetry invented by Heisenberg (1932). Isospin symmetry is due the near equality of the masses of the proton and neutron. Mn ≈ Mp (Mn = 1, Mp = .99826 The strong interaction does not distinguish between the neutron and proton. Consider the neutron and proton to be identical particles (nucleons) that can be found in two states. It does not feel (couple) to electric charge. Charge independence of the nuclear force. POSTULATE: Isospin is conserved in the strong interaction but not in the electromagnetic or weak interaction. ISOSPIN- SU(2) NUCLEON: PROTON p, POSITIVE CHARGE NEURON n, NO CHARGE MASS OF PROTON ≈ MASS OF NEUTRON FORGET CHARGE-TURN OFF ELECTRO-MAGNETIC INTERACTION PROTON AND NEUTRON ARE TWO DIFFERENT “STATES” OF SAME PARTICLE 0 1 1 0 1 0 0 1 p → n, The mathematical idea is correct-However proton decay is a consequence of a grand unified theory, is totally hypothetical and has never been observed. QUARK MODEL qqq BARYONS qq ̄ MESONS THE BARYON DECUPLET PREDICTED 1962 FOUND 1964 THE MESON OCTET NEUTRON BETA DECAY - n → p + e + ϒe - udd→ udu + e + ϒe → ⅔ + (- ⅓) + ⅔ + -1 + 0 CONSERVATION OF ELECTRIC CHARGE WEAK INTERACTION • Extremely short range 10-17 m • Strength of about 10-5 Compare this with the Electromagnetic coupling; α = 10-2 • There are three boson particles (force particles). • It is responsible for radioactive decay of atoms. • In 1933, Enrico Fermi proposed the first theory of the weak interaction. GLASHOW WEINBERG SALAM ELECTROWEAK THEORY UNIFIES THE ELECTROMAGNETIC AND WEAK INTERACTION- ALTHOUGH COUPLING STRENGTHS ARE VERY DIFFERENT. PREDICTS THE EXISTENCE OF THREE NEW GAUGE BOSONS (FORCE PARTICLES) INCLUDES THE PHOTON OF ELECTROMAGNETIC THEORY THREE KINDS OF WEAK INTERACTION- LEPTON-LEPTON, LEPTON -HADRON, HADRON-HADRON EXPERIMENTS SHOW ONLY LEFT HANDED PARTICLES OR THEIR RIGHT HANDED ANTIPARTICLES FEEL THE WEAK FORCE. BUT THERE IS A SERIOUS PROBLEM: THE THREE GAUGE BOSONS (FORCE PARTICLES) HAVE MASS. GAUGE THEORIES MUST HAVE MASSLESS FORCE PARTICLES LIKE THE PHOTON. SLIDES 38, 39 from ‘The Cosmic Onion’ Frank Close LEE AND YANG 1956- ‘IS PARITY CONSERVED IN THE WEAK INTERACTION?” MADAME WU’S EXPERIMENT WITH COBALT 60 THE ELECTRONS EMITTED TEND TO GO IN A PREFERRED DIRECTION CONSERVATION OF PARITY FAILS IN THE WEAK INTERACTION CHIRAL PHENOMENON: one that is not identical to its mirror image- the electrons are chiral fermions Will the parity transformed car (everything parity transformed) go in the reverse direction? Extended Weak Bonding Interactions in DNA: π-Stacking (Base−Base), Base−Backbone, and Backbone−Backbone Interactions† Chérif F. Matta, Norberto Castillo, and Russell J. Boyd* Department of Chemistry, Dalhousie University, Halifax, Nova Scotia, Canada B3H 4J3 J. Phys. Chem. B, 2006, 110 (1), pp 563–578 “We report on several weak interactions in nucleic acids, which, collectively, can make a nonnegligible contribution to the structure and stability of these molecules.” CHARGE CONJUGATION (C-SYMMETRY) A transformation that switches all particles with their corresponding antiparticles and thus changes the sign of all charges; not only electric charge but also the charges relevant to other forces. Electromagnetism, gravity and the strong interaction all obey C-symmetry. Weak interactions violate C-symmetry. TIME REVERSAL (T-SYMMETRY ) A transformation in which time runs backward. It implies that the same laws of physics apply equally well going forward in time or backward. Since the second law of thermodynamics means that entropy increases as time flows toward the future, the universe does not in general show symmetry under time reversal. Time is said to be non-symmetric, or asymmetric. TIME-REVERSAL ASYMMETRY in particle physics has finally been clearly seen (1964) in the Weak Interaction.
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