Modern cosmology has sharpened questions posed for millennia about the origin of our cosmic habitat. The age-old questions have been transformed into two pressing issues primed for attack in the coming decade: How did the Universe begin? and What phy
sical laws govern the Universe at the highest energies? The clearest window onto these questions is the pattern of polarization in the Cosmic Microwave Background (CMB), which is uniquely sensitive to primordial gravity waves. A detection of the special pattern produced by gravity waves would be not only an unprecedented discovery, but also a direct probe of physics at the earliest observable instants of our Universe. Experiments which map CMB polarization over the coming decade will lead us on our first steps towards answering these age-old questions.
The Source Galerkin method finds approximate solutions to the functional differential equations of field theories in the presence of external sources. While developing this process, it was recognized that approximations of the spectral representation
s of the Greens functions by Sinc function expansions are an extremely powerful calculative tool. Specifically, this understanding makes it not only possible to apply the Source Galerkin method to higher dimensional field theories, but also leads to a new approach to perturbation theory calculations in scalar and fermionic field theories. This report summarizes the methodologies for solving quantum field theories with the Source Galerkin method and for performing perturbation theory calculations using Sinc approximations.
The Source Galerkin Method is a new numerical technique that is being developed to solve Quantum Field Theories on the continuum. It is not based on Monte Carlo techniques and has a measure to evaluate relative errors. It promises to increase the acc
uracy and speed of calculations, and takes full advantage of symmetries of the theory. The application of this method to the non-linear sigma model is outlined.
