Physics 467

My notes in pdf form.

See chapter 13 for my notes on the binomial, Poisson, and gaussian distributions.

To view a video of one of the lectures, you should download its wmv file to your computer and view it there.

Video of first lecture on group theory.

Video of second lecture on group theory.

Video of third lecture on group theory.

Video of fourth lecture on group theory.

Video of fifth lecture on group theory: structure constants, the Jacobi identity, and the adjoint representation.

Video of sixth lecture on group theory: SU(3) and quarks, the classical and exceptional groups, the standard model of particle physics.

Video of first lecture on tensors: points and coordinate systems, contravariant and covariant vectors, special relativity.

Video of second lecture on tensors: Lorentz transformations, muon cosmic rays, tensors, tensor equations, the quotient rule.

Video of third lecture on tensors: the metric tensor, covariant derivatives, Christoffel symbols.

Video of fourth lecture on tensors: the covariant curl, the covariant derivative of the metric tensor, the divergence of a contravariant vector, the laplacian

Videos of first and second parts of fifth lecture on tensors:

equations of motion of particles in electromagnetic and gravitational fields, and in weak static gravitational fields, gravitational time dilation, the Pound-Rebka experiment, curvature, Einstein's equations, Schwarzschild's solution, and black holes.

Video of a lecture on gauge theory: abelian and nonabelian gauge theory, the standard model.

Video of lecture on strings and finance:

the problem of infinities in quantum field theory, the Nambu-Goto action, Dp-branes and why we don't see the extra dimensions, and some advice on trading stocks.

Course description.

My e-mail address is cahill@unm.edu. My cell phone is 205 5448.

Xuefeng Zhang zxf@unm.edu is the grader.

Srinivasa Ramanujan's approximation for the natural logarithm of n! is better than Stirling's.

First homework assignment: Show that the variance of the binomial distribution is pqN. Show that the solution of the diffusion equation satisfies that equation. Take the Poisson limit of the gaussian distribution. Use Ramanujan's formula to cast the binomial distribution into a form without factorials.

Solutions to the first set of homework problems.

Second homework assignment: do all these problems.

Solutions to the second set of homework problems.

Ott's introduction to chaos.

Handwritten notes on integrable systems. Ott's discussion of hamiltonian systems.

Third homework assignment: do all the problems at the end of the chapter (2) on group theory in the class notes.

Solutions to the third set of homework problems.

Chapters 3, 4, 5, 6, 7, 8, 9, 10.1, 10.2, and 14 of The Structure of Economics: A Mathematical Analysis by E. Silberberg and W. Suen (McGraw-Hill Higher Education, New York US, third edition, 2001. ISBN: 9780072343526). This textbook is wordy with elementary mathematics.