Renormalization group in the internal space consists of the gradual change of the coupling constants. Functional evolution equations corresponding to the change of the mass or the coupling constant are presented in the framework of a scalar model. The evolution in the mass which yields the functional generalization of the Callan-Symanzik equation for the one-particle irreducible effective actio...

The adiabatic connection can be used in density functional theory to define the unknown ~exchange and! correlation density functional. Using conventional wave-function techniques, accurate estimates of thus defined ~exchange and! correlation energy densities can be obtained for specified systems. In this paper, numerical results are presented for the He and the Be atom, as well as the isoelectr...

A value of the cosmological constant in a toy model of the five-dimensional universe is calculated in such a manner that it remains in agreement with both astronomical observations and the quantum field theory concerning the zero-point fluctuations of the vacuum. The (negative) cosmological constant is equal to the inverse of the Planck length squared, which means that in the toy model the vani...

The hypothesis of this paper is that there is a quantum integer number system that is analogous to the numbers associated with the elements, the isotopes, or the different energy states of hydrogen. The quantum numbers in this new model are instead associated with different fundamental constants (i.e. the normalized properties of hydrogen, or masses of particles and bosons) rather than to a spe...

It is shown how grand unification can occur in models which are partly supersymmetric. The particle states which are composite do not contribute to the running of gauge couplings above the compositeness scale, while the elementary states contribute the usual large logarithmns. This introduces a new differential running contribution to the gauge couplings from partly composite SU(5) matter multi...

We derive compact analytical formulae of the Bonneau-Martin type for the reaction e + e − → ¯ f f γ with cuts on minimal energy and acollinearity of the fermions, where the photons may be emitted both from the initial or final states. Soft-photon exponentiation is also taken into account. One of the cleanest scattering processes at elementary particle accelerators is fermion-pair production in ...

We derive compact analytical formulae of the Bonneau-Martin type for the reaction e + e − → ¯ f f γ with cuts on minimal energy and acollinearity of the fermions, where the photons may be emitted both from the initial or final states. Soft-photon exponentiation is also taken into account. One of the cleanest scattering processes at elementary particle accelerators is fermion-pair production in ...

We consider the interaction of gravity, as expressed by Einstein’s Equations of General Relativity, to other force fields. We describe some recent results, discussing both the mathematics, and the physical interpretations. These results concern both elementary particles, as well as cosmological models. (This paper describes joint work variously done with with F. Finster, N. Kamran, B. Temple, a...

These proceedings summarize lectures that were delivered as part of the 2002 and 2003 Theoretical Advanced Study Institutes in elementary particle physics (TASI) at the University of Colorado at Boulder. They are intended to provide a pedagogical introduction to cosmology aimed at advanced graduate students in particle physics and string theory.