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Different books use different conventions, and sometimes even my notes
may differ. Here is a possibly useful table.
Here there may appear some notes expanding on explicit pages of the text book:
- but there aren't any such notes yet
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I have written up some notes which may be helpful as a background
in mathematical techniques, and some that give more technical details
of things presented in the lecture notes without all the details.
These are notes on mathmatical techniques which should be part of your
background. Some are not directly relevant to this course.
- Notes on using indices correctly: “On Indices and
Arguments”:
(view) or (print).
Some cautionary notes on how indices are used and how to avoid
making nonsense when evaluating expressions with dummy indices.
This seems trivial, but I have seen many students have difficulties.
- Using ε's and determinants
- εijk and cross products
in 3-D Euclidean space:
Notes on totally antisymmetric tensors, or Levi-Civita symbols,
(view),
(print)
- εμνρ... in higher dimensional
Euclidean or Minkowski space:
(view),
(print),
including their use with matrices and determinants. The
Levi-Civita symbol is also essential in curved spaces, but that is
for another course.
Also, on ε and determinants, "Properties of Determinants":
(view),
(print)
- Differentials
- The gradient operator view
or print.
- On differential forms. If you have not seen differential forms
before, you might want to look at
my notes from 507, pages 153-4 on 1-forms and pp 167-175 on
higher k-forms, or
Zapolsky's notes.
They are discussed in advanced calculus texts, e.g.
Buck, "Advanced Calculus".
- Vector Identities from cover of
Jackson, or all on one
sheet version.
- The beta function B(x,y) and Γ(ε) for ε ≅ 0:
view or
print.
- Note on the Surface "Area" of a D-dimensional ball, and on the Euler
Γ function: “Γ(N/2) and the Volume
of SD-1”: (view or
print).
- Notes on Bessel functions (view or
print), giving in particular the
orthonormality properties.
- Notes on Lie Algebras and Groups:
You really ought to take a course on group theory, but if
you haven't, here are
- “ Lightning review of groups”:
(view or
print).
Their definition and representations, the connection of continuous
groups to Lie algebras, Killing forms and Casimir operators.
- “Note on Representations, the Adjoint rep, the Killing
form, and antisymmetry of cijk”:
(view or
print).
Here are some notes that go a bit beyond what we discussed in class.
- Extra note on Noether's Theorem:
view
or print.
- Stress-Energy tensor for Maxwell Theory:
view
or print.
- Schwinger trick and Feynman Parameters:
view or
print.
- A “Little Note on Fierz”:
view or
print.
Joel Shapiro
(shapiro@physics.rutgers.edu)
Last modified: Wed Mar 26 12:16:43 2014
