30 research outputs found
Nonrelativistic hydrogen type stability problems on nonparabolic 3-manifolds
We extend classical Euclidean stability theorems corresponding to the
nonrelativistic Hamiltonians of ions with one electron to the setting of non
parabolic Riemannian 3-manifolds.Comment: 20 pages; to appear in Annales Henri Poincar
Once more on the Witten index of 3d supersymmetric YM-CS theory
The problem of counting the vacuum states in the supersymmetric 3d
Yang-Mills-Chern-Simons theory is reconsidered. We resolve the controversy
between its original calculation by Witten at large volumes and the calculation
based on the evaluation of the effective Lagrangian in the small volume limit.
We show that the latter calculation suffers from uncertainties associated with
the singularities in the moduli space of classical vacua where the
Born-Oppenheimer approximation breaks down. We also show that these
singularities can be accurately treated in the Hamiltonian Born-Oppenheimer
method, where one has to match carefully the effective wave functions on the
Abelian valley and the wave functions of reduced non-Abelian QM theory near the
singularities. This gives the same result as original Witten's calculation.Comment: 27 page
Investigation on the photoconductive behaviors of an individual AlN nanowire under different excited lights
Experimental and theoretical insights into photochemical transformation kinetics and mechanisms of aqueous propylparaben and risk assessment of its degradation products
Infinite dimensional degree theory and Ramer's finite co-dimensional differential forms
Infinite-dimensional degree theory, especially for Fredholm maps with positive index as developed with Tromba, is combined with Ramer’s unpublished thesis work on finite co-dimensional differential forms. As an illustrative example, the approach of Nicolaescu and Savale to the Gauss–Bonnet–Chern theorem for vector bundles is reworked in this framework. Other examples mentioned are Kokarev and Kuksin’s approach to periodic differential equations and to forced harmonic maps. A discussion about how such forms and their constructions and cohomology relate to constructions for diffusion measures on path and loop spaces is also included