The Renormalization Group for Flag Manifolds

The renormalization group equations for a class of non--relativistic quantum $\sigma$--models targeted on flag manifolds are given. These models emerge in a continuum limit of generalized Heisenberg antiferromagnets. The case of the ${SU(3)\over U(1)\times U(1)}$ manifold is studied in greater detail. We show that at zero temperature there is a fixed point of the RG transformations in $(2+\varepsilon )$--dimensions where the theory becomes relativistic. We study the linearized RG transformations in the vicinity of this fixed point and show that half of the couplings are irrelevant. We also show that at this fixed point there is an enlargement of the global isometries of the target manifold. We construct a discrete non--abelian enlargement of this kind.Comment: 22 page

Continuous Local Symmetry in Ising-type Models

A class of generalized Ising models is examined with a view to extracting a low energy sector comprising Dirac fermions coupled to Yang-Mills vectors. The main feature of this approach is a set of gap equations, covariant with respect to one of the $4$-dimensional crystallographic space groups.Comment: 7 pages, latex, IC/94/2

Dissociative Autoionization in (1+2)-photon Above Threshold Excitation of H2 Molecules

We have theoretically studied the effect of dissociative autoionization on the photoelectron energy spectrum in (1+2)-photon above threshold ionization(ATI) of H2 molecules. We have considered excitation from the ground state X-singlet-Sigma-g+(v=0,j) to the doubly excited autoionizing states of singlet-Sigma-u+ and singlet-Pi-u+ symmetry, via the intermediate resonant B-singlet-Sigma-u+(v=5,j) states. We have shown that the photoelectron energy spectrum is oscillatory in nature and shows three distinct peaks above the photoelectron energy 0.7 eV. This feature has been observed in a recent experiment by Rottke et al, J. Phys. B, Vol. 30, p-4049 (1997).Comment: 11 pages and 4 figure

Stigma as a fundamental hindrance to the United States opioid overdose crisis response.

Alexander Tsai and co-authors discuss the role of stigma in responses to the US opioid crisis

Consistent and covriant anomalies in the overlap formulation of chiral gauge theories

In this letter we show how the covariant anomaly emerges in the overlap scheme. We also prove that the overlap scheme correctly reproduces the anomaly in the flavour currents such as $j^5_\mu$ in vector like theories like QCD.Comment: 10 pages, Late

On the Overlap Prescription for Lattice Regularization of Chiral Fermions

Feynman rules for the vacuum amplitude of fermions coupled to external gauge and Higgs fields in a domain wall lattice model are derived using time--dependent perturbation theory. They have a clear and simple structure corresponding to 1--loop vacuum graphs. Their continuum approximations are extracted by isolating the infrared singularities and it is shown that, in each order, they reduce to vacuum contributions for chiral fermions. In this sense the lattice model is seen to constitute a valid regularization of the continuum theory of chiral fermions coupled to weak and slowly varying gauge and Higgs fields. The overlap amplitude, while not gauge invariant, exhibits a well defined (modulo phase conventions) response to gauge transformations of the background fields. This response reduces in the continuum limit to the expected chiral anomaly, independently of the phase conventions.Comment: 32 pages, late

Gravitational Lorentz anomaly from the overlap formula in 2-dimensions

In this letter we show that the overlap formulation of chiral gauge theories correctly reproduces the gravitational Lorentz anomaly in 2-dimensions. This formulation has been recently suggested as a solution to the fermion doubling problem on the lattice. The well known response to general coordinate transformations of the effective action of Weyl fermions coupled to gravity in 2-dimensions can also be recovered.Comment: 7 pages, late