Algebraic Properties of BRST Coupled Doublets

We characterize the dependence on doublets of the cohomology of an arbitrary nilpotent differential s (including BRST differentials and classical linearized Slavnov-Taylor (ST) operators) in terms of the cohomology of the doublets-independent component of s. All cohomologies are computed in the space of local integrated formal power series. We drop the usual assumption that the counting operator for the doublets commutes with s (decoupled doublets) and discuss the general case where the counting operator does not commute with s (coupled doublets). The results are purely algebraic and do not rely on power-counting arguments.Comment: Some explanations enlarged, references adde

Wess-Zumino Terms for Reducible Anomalous Gauge Theories

Reducible off-shell anomalous gauge theories are studied in the framework of an extended Field-Antifield formalism by introducing new variables associated with the anomalous gauge degrees of freedom. The Wess-Zumino term for these theories is constructed and new gauge invariances appear. The quantum effects due to the extra variables are considered.Comment: 31 pages, Latex file, no figures. Section added. To appear in Nucl.Phys.

Generalized Classical BRST Cohomology and Reduction of Poisson Manifolds

In this paper, we formulate a generalization of the classical BRST construction which applies to the case of the reduction of a poisson manifold by a submanifold. In the case of symplectic reduction, our procedure generalizes the usual classical BRST construction which only applies to symplectic reduction of a symplectic manifold by a coisotropic submanifold, \ie\ the case of reducible ``first class'' constraints. In particular, our procedure yields a method to deal with ``second-class'' constraints. We construct the BRST complex and compute its cohomology. BRST cohomology vanishes for negative dimension and is isomorphic as a poisson algebra to the algebra of smooth functions on the reduced poisson manifold in zero dimension. We then show that in the general case of reduction of poisson manifolds, BRST cohomology cannot be identified with the cohomology of vertical differential forms.Comment: 3

The Logic and Limits of Event Studies in Securities Fraud Litigation

Event studies have become increasingly important in securities fraud litigation, and the Supreme Court’s 2014 decision in Halliburton Co. v. Erica P. John Fund, Inc. heightened their importance by holding that the results of event studies could be used to obtain or rebut the presumption of reliance at the class certification stage. As a result, getting event studies right has become critical. Unfortunately, courts and litigants widely misunderstand the event study methodology leading, as in Halliburton, to conclusions that differ from the stated standard. This Article provides a primer explaining the event study methodology and identifying the limitations on its use in securities fraud litigation. It begins by describing the basic function of the event study and its foundations in financial economics. The Article goes on to identify special features of securities fraud litigation that cause the statistical properties of event studies to differ from those in the scholarly context in which event studies were developed. Failure to adjust the standard approach to reflect these special features can lead an event study to produce conclusions inconsistent with the standards courts intend to apply. Using the example of the Halliburton litigation, we illustrate the use of these adjustments and demonstrate how they affect the results in that case. The Article goes on to highlight the limitations of event studies and explains how those limitations relate to the legal issues for which they are introduced. These limitations bear upon important normative questions about the role event studies should play in securities fraud litigation

Topological Defects in the Random-Field XY Model and the Pinned Vortex Lattice to Vortex Glass Transition in Type-II Superconductors

As a simplified model of randomly pinned vortex lattices or charge-density waves, we study the random-field XY model on square ($d=2$) and simple cubic ($d=3$) lattices. We verify in Monte Carlo simulations, that the average spacing between topological defects (vortices) diverges more strongly than the Imry-Ma pinning length as the random field strength, $H$, is reduced. We suggest that for $d=3$ the simulation data are consistent with a topological phase transition at a nonzero critical field, $H_c$, to a pinned phase that is defect-free at large length-scales. We also discuss the connection between the possible existence of this phase transition in the random-field XY model and the magnetic field driven transition from pinned vortex lattice to vortex glass in weakly disordered type-II superconductors.Comment: LATEX file; 5 Postscript figures are available from [email protected]

On the Critical Temperature of Non-Periodic Ising Models on Hexagonal Lattices

The critical temperature of layered Ising models on triangular and honeycomb lattices are calculated in simple, explicit form for arbitrary distribution of the couplings.Comment: to appear in Z. Phys. B., 8 pages plain TEX, 1 figure available upon reques

Magnetic field generation through angular momentum exchange between circularly polarized radiation and charged particles

The interaction between circularly polarized (CP) radiation and charged particles can lead to generation of magnetic field through an inverse Faraday effect. The spin of the circularly polarized electromagnetic wave can be converted into the angular momentum of the charged particles so long as there is dissipation. We demonstrate this by considering two mechanisms of angular momentum absorption relevant for laser-plasma interactions: electron-ion collisions and ionization. The precise dissipative mechanism, however, plays a role in determining the efficiency of the magnetic field generation

One Loop Anomalies and Wess-Zumino Terms for General Gauge Theories

One loop anomalies and their dependence on antifields for general gauge theories are investigated within a Pauli-Villars regularization scheme. For on-shell theories {\it i.e.}, with open algebras or on-shell reducible theories, the antifield dependence is cohomologically non trivial. The associated Wess-Zumino term depends also on antifields. In the classical basis the antifield independent part of the WZ term is expressed in terms of the anomaly and finite gauge transformations by introducing gauge degrees of freedom as the extra dynamical variables. The complete WZ term is reconstructed from the antifield independent part.Comment: 15 pages, An example of non-abelian antisymmetric field is added. Some corrections are made to refrain from using the reconstruction theorem in the gauge fixed basi

The unphysical nature of the SL(2,R) symmetry and its associated condensates in Yang-Mills theories

BRST cohomology methods are used to explain the origin of the SL(2,R) symmetry in Yang-Mills theories. Clear evidence is provided for the unphysical nature of this symmetry. This is obtained from the analysis of a local functional of mass dimension two and constitutes a no-go statement for giving a physical meaning to condensates associated with the symmetry breaking of SL(2,R).Comment: 5 pages (revtex4), final version to appear in Phys. Rev.