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Physics 618, Spring 2017


The syllabus is subject to change, often without advance notice, but the changes will probably be small, except for the timing, and with new material added.

My materials are generally available in view mode (one page per side, for viewing) and in print mode (two pages per side, for more efficient printing).

The textbooks for the course are not required, as there are many alternatives available, and all the material will be covered in my lecture notes, which are posted, both here and on the Lecture Notes page. Nonetheless, you should have some textbook that covers this material. The leading contenders are

  • H. F. Jones, Groups, Representations and Physics . The newer, (1998) edition has some additional material, but not in the sections we will use.
  • Howard Georgi Lie Algebras in Particle Physics Probably best to have Second (1999) Edition.
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What appears below the dividing line is mostly the syllabus from 2016, and at best tentative. What is above the dividing line has been revised for 2017.

The readings listed are from my notes, listed by chapter names or numbers. Material below the line may be changed later, however.

Click on a date with a pale green background to get the introductory comments for the lecture

  Date Topic Reading
    Cover and Table of Contents: view or print, pages 1-4
L1 1/17 Symmetries and groups, subgroups, morphisms, measures Groups: view or print, pages 7-17
L2 1/20 conjugacy, cosets, Cn, normal subgroups, permutations, small groups Groups, pages 17-26
L3 1/24 Representations, reducibility, Schur's first and second lemmas Reps: view or print, pages 25-34
H11/26 Homework Assignment # 1: view or print.
L4 1/27 Great Orthogonality Theorem, regular rep, characters, orthog on classes Reps, pages 34-41
H22/2 Homework Assignment # 2: view or print.
L5 1/31 Characters of D4. Point and crystalographic groups. Direct products of reps. Reps, pages 41-48
L6 2/3 Infinite Groups, Lie Groups, connectedness, generators, structure constants Reps. pages 49-56
Lie view or print. Pages 47-56
H32/7 Homework Assignment # 3: view or print.
L7 2/7 Lie Algebra, group manifolds Adjoint rep, Killing form, semisimple, Poincaré group, Lie pages 56-64
H42/16 Homework Assignment # 4: view or print.
L8 2/10 Quantum Operators; SU(2): Cartan subalgebra; raising and lowering ops. Weights. Direct products Lie pages 64-66,
SU(2) view or print. Pages 67-71
L9 2/14 Vector coupling coefs SU(2) pages 71-78
L10 2/17 Wigner-Eckhart; Isospin, Weight and root vectors, Angles between roots SU(2): 78-83, SS Compact: view or print, pages 85-86
L11 2/21 SU(3) Gell-Mann matrices, quark and octet reps. Ordering roots. SS Compact: pages 87-93;
SU(3): view or print, pages 91-93
H52/23 Homework Assignment # 5: view or print.
L12 2/24 G2, Dynkin Diagrams Simple Roots view or print, pages 95-98
Dynkin: view or print, pages 99-101
L13 2/28 Finding the Other Roots. Irreducible Reps of Lie Groups Dynkin 102-104; OtherRoots: view or print, pages 105-107 LieReps: view or print, pages 109-110
H63/2 Homework Assignment # 6: view or print.
L14 3/3 Highest weights, fundamental reps, tensor methods LieReps: pages 110-116;
Exam3/7 Midterm Exam Chapters 1-8 1/2, pp 5-107.
L15 3/10 SU(3) reps, dimensions; Group algebra, Sk LieReps: pages 117-119; PermReps: view or print, pages 121-124
L16 3/21 Young tableaux, Sk reps PermReps: view or print, pages 124-132
H73/23 Homework Assignment # 7: view or print.
L17 3/24 Representations of SU(N) PermReps: 122-128
L18 3/28 Tensor products of SU(N) reps; Field Theory Tensor: view or print, pages 129-132
classMech: view or print, pages 1-8
L19 3/31 Intro to Gauge groups, Gauge fields, field strength tensor LocalSym: view or print, pages 133-145
L20 4/4 Gauge Invariance. Hamiltonian formulation LocalSym: pages 142-151
Hamil: view or print pages 147-154
H84/6 Homework Assignment # 8: view or print.
L21 4/7 Canonical momenta, Left and Right derivative operators Hamil: pp 154-161
Below this line is left over from 2016 and may change
L22 4/11 Haar measure. Phonons, Bloch waves, SSB Hamil: pp 161-162; BlockSSB: view or print, pages 163-166
L23 4/14 SSB and the Higgs Mechanism SSB and Higgs: view or print, pages 171-173
L24 4/18 The standard model SSB and Higgs pp 173-178
L25 4/21 Fermions in the Standard Model SSB and Higgs pp 178-188
L26 4/25 Poincare and SU(6); SUSY PoinSUSY: view or print, pages 188-192
L27 4/28 Superfields PoinSUSY: pages 193-201
Exam5/4 Final Exam, noon - 3:00, SEC room 206 Chapters 1-17

  Joel Shapiro (
  Last modified: Wed Apr 26 10:56:44 2017