A GRAND TOUR OF PHYSICS

DR. GEORGE DERISE PROFESSOR EMERITUS, MATHEMATICS THOMAS NELSON COMMUNITY COLLEGE SPRING 2019

APR. 12, 2019 1:30 – 3:30 TNCC ROOM 328.

PARTICLE PHYSICS

LECTURE 4

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

COUPLING CONSTANT STRENGTH α= 1/137

SOLID LINES - ELECTRONS (WAVEFUNCTIONS)- MATTER PARTICLES; FERMIONS WAVY (OR DASHED) LINE - PHOTON - FORCE PARTICLE; BOSON

The infinite series S converges to 2. S=2.

The infinite series above diverges to ∞

INFINITE SERIES EXPANSIONS

𝑀 = 1 +1

102+

1

104+

1

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 = . . . −𝟑,−𝟐,−𝟏, 𝟎, +𝟏,+𝟐,+𝟑. . . 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

e-, μ-, τ- THREE LEPTONS- ELECTRON, MUON, TAU

(ASSUME THEY HAVE THE SAME MASS)

A HYPOTHETICAL WORLD

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.

? → CHARGE CONSERVATION

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.

SPACETIME GROUPS

3+3+1+3=10

EACH A SUBGROUP OF THE 10 DIMENSIONAL POINCARÉ GROUP

ALGEBRA OF MINKOWSKI SPACETIME- SPECIAL RELATIVITY

MATH Given, a length L at A Apply a rigid body transformation T Length L before at A Equals the length L after at B Implies Conservation of distance (Euclidean Geometry)

PHYSICS Given, a wave function ѱ(x). Shift the phase of ѱ in the Lagrangian L Lagrangian L before equals the Lagrangian L after This implies Conservation of Electric Charge (Electrodynamics)

WHAT IS THE SYMMETRY THAT IMPLIES CHARGE CONSERVATION ?

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 HAS AN AMPLITUDE AND A PHASE.

THE WAVE FUNCTION IS THE SOLUTION OF SCHRÖDINGER’S EQUATION.

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 point on the circle by the same amount everywhere in space, then the laws of physics should be the same: Conserved quantity electric charge

A LOCAL GAUGE SYMMETRY, however, is one where we can do an independent rotation at each point in space (i.e. A LOCAL TRANSFORMATION): If a symmetry is a gauge symmetry, then this 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

𝝍electron  =  𝝍𝟏 + 𝒊𝝍𝟐 𝟐

𝝍positron  =  𝝍𝟏  − 𝒊𝝍𝟐 𝟐

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

udd→ udu + e- + ϒe

n → p + 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

CONSERVATION OF PARITY FAILS IN THE WEAK INTERACTION

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

CHIRAL PHENOMENON: one that is not identical to its mirror image- the electrons are chiral fermions

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.”

Will the parity transformed car (everything parity transformed) go in the reverse direction?

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.

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.

Electromagnetism, gravity and the strong interaction all obey C-symmetry. Weak interactions violate C-symmetry.

TIME-REVERSAL ASYMMETRY in particle physics has finally been clearly seen (1964) in the Weak Interaction. Physics Today Nov. 2012

CHARGE, PARITY, AND TIME REVERSAL SYMMETRY (CPT)- A FUNDAMENTAL SYMMETRY OF PHYSICAL LAWS under the simultaneous transformations of charge conjugation (C), parity transformation (P), and time reversal (T).

CPT IS THE ONLY COMBINATION OF C, P, AND T THAT IS OBSERVED TO BE AN EXACT SYMMETRY OF NATURE AT THE FUNDAMENTAL LEVEL. arXiv:hep-ph/9810365

HIGGS MECHANISM: Ball on top perfect symmetry particles -zero mass Ball in valley spontaneous symmetry breaking particles get mass

The Full Standard Model Lagrangian will describe every physical interaction in the universe. H is the Higgs boson.

1ST RED TERM: HIGGS HAS MASS

LHC LARGE HADRON COLLIDER at CERN

The largest machine in the world 17mi. vacuum as empty as interplanetary space more than 100 000 times hotter than the Sun most powerful supercomputer system in the world

trillions of protons race around the LHC ring 11 245 times a second, travelling at 99.9999991% the speed of light. super cool temperature of -271.3°C colder than outer space

http://public.web.cern.ch/public/en/lhc/Facts-en.html

4th July 2012: CERN announces discovery of a new particle, consistent with the Higgs boson.

(The ACTION)

125.3 126

QUARK MODEL SU(3) QUANTUM CHROMODYNAMICS

ASYMPTOTIC FREEDOM: The color force between quarks becomes vanishingly small as the quarks come close together.

A steady reduction in the strength of interactions between quarks and gluons as the energy scale of those interactions increases and the corresponding length scale decreases. Discovered in 1973.

COLOR CONFINEMENT: (INFRARED SLAVERY) The nucleons (proton and neutron) are extremely strongly bound aggregates of quarks: so strongly bound that we have never seen a free quark. The color force at large distances becomes stronger.

In order to increase the separation between two quarks within a hadron, ever-increasing amounts of energy are required. Eventually this energy produces a quark–antiquark pair, turning the initial hadron into a pair of hadrons instead of producing an isolated color charge. Although analytically unproven, color confinement is well established from decades of experiments.

THE STANDARD MODEL OF PARTICLE PHYSICS

SU(3) x SU(2) x U(1)

THE STANDARD MODEL OF PARTICLE PHYSICS: the theory describing three of the four known fundamental forces in the Universe, as well as classifying all known elementary particles. It is a consistent theoretical structure to explain ‘the Particle Zoo’.

Developed in the early 1970s, it has successfully explained almost all experimental results; it precisely predicted a wide variety of phenomena. Its predictions have matched experimental data with amazing precision.

PET SCAN actually uses antiparticles injected into the body. MRI for better imaging. PROTON THERAPY uses protons rather than x-rays to treat cancer.

THE STANDARD MODEL

SU(3) x SU(2) x U(1) STANDARD MODEL OF PARTICLE PHYSICS

STANDARD MODEL; WHAT’S WRONG 1. THREE INDEPENDENT COUPLING CONSTANTS, WHY THEIR VALUES?

2. FAMILY PROBLEM; WHY 3 FAMILIES OF QUARKS AND LEPTONS?

3. HIGGS MECHANISM

4. WHY THE MASSES OF THE PARTICLES?

5. WHY CP SYMMETRY BREAKING IN WEAK INTERACTION-NOT IN STRONG

6. TOO MANY ARBITRARY PARAMETERS

7. WHY DOES THIS MODEL WORK?

8. WHY IS THERE MORE MATTER THAN ANTIMATTER?

9. WHAT ABOUT DARK MATTER? DARK ENERGY?

10. HIERARCHY PROBLEM; WHY m(H)<< m(PLANCK)

DOES NOT INCLUDE GRAVITY!