Outline

This is a summary of what we covered both in the classroom and from the book.  The exact time line may not be correct since we sometimes reviewed and extended material covered in earlier lectures.

LECTURE

• Week 1 (1,2,3)
• Review of basic ideas:
• solutions to classical equations orbits
• what is a particle
• what is an interaction
• Newton’s laws
• Space-time
• What are waves
• Interference
• Fourier transforms (frequency-time relationship)
• Vectors, vector mathematics
• Vectors , Four vectors, Tensors ,Rotations
• Groups
• collection of objects such as rotations.
• Members of a group can be combined (successive rotations)
• Identity and inverse
• Combinations can be represented as a single group member (a sum of rotations can be considered as one single rotation)
• Rotations,
• translations (space and time),
• Lorentz and Galilean velocity transformations.
• Recognized that vectors could be defined by their transformation properties.
•

·       Reviewed matrix representations

o      Row and column vectors

o      3x3 matrices

o      4x4 matrices

·       Formulation of relativity.

o      Four vectors

o      Lorentz transformation

o      Field tensor Fμν

• Week 2 (4,5,6)
• Quantum mechanics
• Quantum states form a vector space (Hilbert space).

·       A QS can be written as a linear combination of other QS.

o      Tuning forks can be represented as a string of local pressures (snaps)

o      Snaps can be decomposed using the Fourier transform (tuning forks)

·       Certain sets of states can form  a basis

·       As vectors one can compute an inner product.

o      Orthogonality: No overlap between QS. This implies that the states are chosen to be completely distinct in some way. There is a label that can be used to completely distinguish state 1 and state 2.

o      Overlap: State can share some characteristic. Two states may both have some likelihood of being at some location.

·       Operators may represent observables so their behavior and interpretation tells us how to think about particle properties.

o      Interference

o      Labeling states

o      Two slit, photon polarization

o      What are quanta: Observations or measurements will record many discrete quantities rather than a continuum

o      Amplitudes: To account for the wave nature of QM amplitudes are used.

o      Hilbert space: quantum states as vectors.

Week 3 (7,8,9)

• Quantum (clarification of the above points)
• General relativity
• Bending of space and time as the understanding of an interaction
• Prelude to the way that particle physics is now formulated. Particle physics is based on similar bending of internal quantum spaces as the understanding of E&M (QED) , weak, [electro weak], Strong (QCD) interactions.
• Non specific general discussion based on a paper.

Week 4 (10,11,12)

• Elementary particles
• Discussion based on Weinberg article

Week 5

• Quarks and leptons
• Lepton number, charm beauty, Strangeness…
• Quark content of hadrons and mesons

Week 6

• Feynman Diagrams

Week 7            First test , review and return test

Week 8 & 9

• More on rotations and SO(3)
• SU(2) isospin and general two component spin
• Grouping particles together as an indication of flavor structure
• Meson octet
• Pion π+ , πo , π-  (triplet)
• Translations

Week 10

• Angular momentum, commuting operators

Week 11

• angular momentum and the raising and lowering operators
• Poincare transformation summary

Week 12

• Parity
• Charge conjugation
• Kaon system

Week 13 Thanksgiving no material covered

Week 14

• Helicty, chirality

Week 15          Review

BOOK

Chapter 1

• Feynman diagrams for QED
• Yukawa interactions (massive particle exchange)
• Particle – hole – antiparticle
• Some example reactions
• Dirac equ. Not covered
• Scattering amplitude Not covered

Chapter 2

• Quarks and leptons
• Leptons
• Pairs
• Neutrino
• Lepton number
• Particle decays
• Fermi interaction
• Quarks
• Pairs
• Beauty, Charm, Isospin
• Pion
• Pion exchange
• Particle interaction examples

Chapter3 (not covered)

Chapter4

• Translation/momentum invariance
• Rotation/angular momentum invariance
• Spin
• Composite systems spin (nucleon, pion…)
• Parity/intrinsic parity
• Charge conjugation/intrinsic charge conjugation
• Composite system parity and charge conjugation
• Time reversal

Chapter 5

• Composite system quantum numbers
• Isospsin
• Mass splitting (not covered)
• Resonances (not covered)
• Quark diagrams –composite objects in Feynman diagrams

Chapter 6

• Charmonium (not covered) know quark content only
• Light mesons
• Qunatum numbers
• Quark content
• Qunatum numbers
• Quark content
• Mass splitting, magnetic moment (not covered)
• Color
• Color singlets (rest not covered)

Chapter 7

• QCD, gluons as exchange particle
• (rest of chapter not covered)

Chapter 8

• weak interaction
• W,Z
• Feynman diagrams
• Quark and leptons pairs (ν), (u,d) …..
• Three generations
• Coupling constant (not covered)
• Selection rules (not covered as such) selection rules are a result of using the correct Feynman diagrams.
• Mass mixing
• Top quark not covered

Chapter 9

• Neutral current
• Correct diagrams (differ from W)
• Do not need the mixed states
• Unification (not covered)
• Number of neutrinos (not covered)
• Gauge invariance (not covered)
• Higgs (not covered)

Chapter 10

• Parity violation
• CP violation
• Kaon system
• Right handed, left handed

Chapter 11 (not covered)

Appendices A,B,C  (not covered)

Appendix D

• isospin