Quantum gravitational contributions to quantum electrodynamics.

Quantum electrodynamics describes the interactions of electrons and photons. Electric charge (the gauge coupling constant) is energy dependent, and there is a previous claim that charge is affected by gravity (described by general relativity) with the implication that the charge is reduced at high energies. However, that claim has been very controversial and the matter has not been settled.

Cosmological constant and quantum gravitational corrections to the running fine structure constant.

The quantum gravitational contribution to the renormalization group behavior of the electric charge in Einstein-Maxwell theory with a cosmological constant is considered. Quantum gravity is shown to lead to a contribution to the running charge not present when the cosmological constant vanishes. This reopens the possibility, suggested by Robinson and Wilczek, of altering the scaling behavior of gauge theories at high energies although our result differs.

Effective Action Approach to Bose-Einstein Condensation of Ideal Gases.

We present a short review of how the effective action formalism, well known in relativistic quantum field theory, can be used to discuss Bose-Einstein condensation of non-relativistic gases. This method lends itself very naturally to an interpretation of Bose-Einstein condensation in terms of symmetry breaking. It also allows for the definition of a very elegant regularization technique involving generalized -functions.