Electric neutron polarizability and eigenspectrum subtraction techniques for disconnected quark loops.

I present an analysis for the mass shift of the neutron in order to obtain the neutron electric polarizability. Neutron electric polarizability can be studied by implementing a static electric field on the lattice. The implementation of this field, though, is non-trivial and the "proper" form for lattice implementation is studied and the various techniques are presented. Separately, I present the development of new techniques to calculate disconnected quark loops; a quantity that is necessary for many different analyzes but has been shown to be computationally intensive. These new techniques, which use Z(N) noise, utilize the eigenspectrum of the quark matrix to reduce statistical error found in disconnected operators.