Exact Path Integrals by Equivariant Cohomology

It is a common belief among field theorists that path integrals can be computed exactly only in a limited number of special cases, and that most of these cases are already known. However recent developments, which generalize the WKBJ method using equivariant cohomology, appear to contradict this folk wisdom. At the formal level, equivariant localization would seem to allow exact computation of phase space path integrals for an arbitrary partition function! To see how, and if, these methods really work in practice, we have applied them in explicit quantum mechanics examples. We show that the path integral for the 1-d hydrogen atom, which is not WKBJ exact, is localizable and computable using the more general formalism. We find however considerable ambiguities in this approach, which we can only partially resolve. In addition, we find a large class of quantum mechanics examples where the localization procedure breaks down completely.Comment: LATE

Applications of current algebra in conformal field theory

In this work, two topics concerning the interplay between current algebra and conformal symmetry in two dimensions are discussed. The construction of a conformal algebra from a current algebra, the Virasoro Master Equation, is presented with analytic and perturbative solutions. Second, N = 2 superconformal models based on supersymmetric current algebras with c > 3 are coupled to two dimensional topological gravity

Rate Control versus Rhythm Control for Atrial Fibrillation after Cardiac Surgery

BACKGROUND Atrial fibrillation after cardiac surgery is associated with increased rates of death, complications, and hospitalizations. In patients with postoperative atrial fibrillation who are in stable condition, the best initial treatment strategy -heart-rate control or rhythm control -remains controversial. METHODS Patients with new-onset postoperative atrial fibrillation were randomly assigned to undergo either rate control or rhythm control. The primary end point was the total number of days of hospitalization within 60 days after randomization, as assessed by the Wilcoxon rank-sum test. RESULTS Postoperative atrial fibrillation occurred in 695 of the 2109 patients (33.0%) who were enrolled preoperatively; of these patients, 523 underwent randomization. The total numbers of hospital days in the rate-control group and the rhythm-control group were similar (median, 5.1 days and 5.0 days, respectively; P = 0.76). There were no significant between-group differences in the rates of death (P = 0.64) or overall serious adverse events (24.8 per 100 patient-months in the rate-control group and 26.4 per 100 patient-months in the rhythm-control group, P = 0.61), including thromboembolic and bleeding events. About 25% of the patients in each group deviated from the assigned therapy, mainly because of drug ineffectiveness (in the rate-control group) or amiodarone side effects or adverse drug reactions (in the rhythm-control group). At 60 days, 93.8% of the patients in the rate-control group and 97.9% of those in the rhythm-control group had had a stable heart rhythm without atrial fibrillation for the previous 30 days (P = 0.02), and 84.2% and 86.9%, respectively, had been free from atrial fibrillation from discharge to 60 days (P = 0.41). CONCLUSIONS Strategies for rate control and rhythm control to treat postoperative atrial fibrillation were associated with equal numbers of days of hospitalization, similar complication rates, and similarly low rates of persistent atrial fibrillation 60 days after onset. Neither treatment strategy showed a net clinical advantage over the other