2 research outputs found
Effective Field Theory for Few-Nucleon Systems
We review the effective field theories (EFTs) developed for few-nucleon
systems. These EFTs are controlled expansions in momenta, where certain
(leading-order) interactions are summed to all orders. At low energies, an EFT
with only contact interactions allows a detailed analysis of renormalization in
a non-perturbative context and uncovers novel asymptotic behavior. Manifestly
model-independent calculations can be carried out to high orders, leading to
high precision. At higher energies, an EFT that includes pion fields justifies
and extends the traditional framework of phenomenological potentials. The
correct treatment of QCD symmetries ensures a connection with lattice QCD.
Several tests and prospects of these EFTs are discussed.Comment: 55 pages, 18 figures, to appear in Ann. Rev. Nucl. Part. Sci. 52
(2002
Spectral Theory for Schrödinger Operators with -Interactions Supported on Curves in
The main objective of this paper is to systematically develop a spectral and
scattering theory for selfadjoint Schr\"odinger operators with
-interactions supported on closed curves in . We provide
bounds for the number of negative eigenvalues depending on the geometry of the
curve, prove an isoperimetric inequality for the principal eigenvalue, derive
Schatten--von Neumann properties for the resolvent difference with the free
Laplacian, and establish an explicit representation for the scattering matrix.Comment: to appear in Annales Henri Poincar