In the absence of charges and currents, Maxwell's equations are invariant under the transformation E′ = E cosθ+B sinθ, B′ = −E sinθ+B cosθ. Using Noether's theorem, we show that the corresponding conserved quantity is proportional to the difference in the number of right and left circularly polarized photons in the field.

‘‘A chain is suspended, both ends at the same elevation, and then one end is released.’’ This familiar problem is studied and the real dynamical behavior is found to be very different from the textbook answer. Results are presented that show that the real chain is largely an energy-conserving system. This gives rise to acceleration of the free end greater than g, and to very large tension at the fixed end.

The equations of motion of an inviscid, infinitely conducting fluid in an electronlagnetic field are transformed into a form s~~i t a b l e for a n action principle. An action principle from which these equations may be derived is found. The conservation laws follo~v from invariance properties of the action. The spacetime invariances lead to the conservation of momentum, energy, angular momentum, and center of mass, while the gauge invariances lead to conservation of mass, a generalization of the Ilel~llholtz vortex theorem of hydrodyan~nics, and the conservation of the volume integrals of A . B and v . B , where A is the vector potential, B is the magnetic induction, and v is the fluid velocity.*From a thesis presented in partial fulfillment of the requirements for the degree of Doctor of Philosophy a t the University of British Columbia, October, 1961.thTow a t

It is pointed out that the usual treatment of the delta function potential in the one-dimensional Dirac equation is incorrect. Steps leading to such incorrect results are identified. The delta function potential is also examined from the limiting case of a nonlocal potential V(x,x′). In this general case, the strength g=∫dx ∫dx′V(x,x′) is no longer a sufficient parameter to characterize a potential.

The motion of a spring, initially suspended from its top end and hanging in equilibrium in the earth’s field, and then released and allowed to fall, is studied. The difference between the behaviors of loosely wound and tightly wound springs is emphasized.