Daniel Cangemi

Physical states in matter-coupled dilaton gravity

We revisit the quantization of matter-coupled, two-dimensional dilaton gravity. At the classical level and with a cosmological term, a series of field transformations leads to a set of free fields of indefinite signature. Without matter the system is represented by two scalar fields of opposite signature. With a particular quantization for the scalar with negative kinetic energy, the system has zero central charge and we find some physical states satisfying {ital all} the Virasoro conditions. With matter, the constraints cannot be solved because of the Virasoro anomaly. We discuss two avenues for consistent quantization: modification of the constraints, and BRST quantization. The first avenue appears to lead to very few physical states. The second, which roughly corresponds to satisfying half of the Virasoro conditions, results in a rich spectrum of physical states. This spectrum, however, differs significantly from that of free matter fields propagating on flat two-dimensional space-time. Copyright {copyright} 1996 Academic Press, Inc.

Self-dual Yang-Mills theory and one-loop maximally helicity violating multi-gluon amplitudes☆

Abstract A scalar cubic action that classically reproduces the self-dual Yang-Mills equations is shown to generate one-loop QCD amplitudes for external gluon all with the same helicity. This result is related to the symmetries of the self-dual Yang-Mills equations.

Poincaré Gauge Theory for Gravitational Forces in (1+1) Dimensions

Abstract We discuss in detail how string-inspired lineal gravity can be formulated as a gauge theory based on the centrally extended Poincare group in (1 + 1) dimensions. Matter couplings are constructed in a gauge invariant fashion, both for point particles and Fermi fields. A covariant tensor notation is developed in which gauge invariance of the formalism is manifest.

Quantal analysis of string inspired lineal gravity with matter fields

Abstract We show that string-inspired lineal gravity interacting with matter fields cannot be Dirac-quantized owing to the well-known anomaly in energy-momentum tensor commutators.

Geometric gravitational force on particles moving in a line

Abstract In two-dimensional space-time, point particles can experience a geometric, dimension-specific gravity force, which modifies the usual geodesic equation of motion and provides a link between the cosmological constant and the vacuum θ-angle. The description of such a force fits naturally into a gauge theory of gravity based on the extended Poincare group, i.e. “string-inspired” dilaton gravity.

One formulation for both lineal gravities through a dimensional reduction

Abstract The two lineal gravities - based on the de Sitter group or a central extension of the Poincare group in 1 + 1 dimension - are shown to derive classically from a unique topological gauge theory. This one is obtained after a dimensional reduction of a Chern-Simons model, which describes pure gravity in 2 + 1 dimensions, the gauge symmetry being given by an extention if ISO (2, 1).

Quantum states of string-inspired lineal gravity

We construct quantum states for a (1+1)-dimensional gravity-matter model that is also a gauge theory based on the centrally extended Poincare group. Explicit formulas are found, which exhibit interesting structures. For example, wave functionals are gauge invariant except for a gauge noninvariant phase factor that is the Kirillov-Kostant one-form on the (co)adjoint orbit of the group. However, no evidence for gravity-matter forces is found.

Temperature Expansions for Magnetic Systems

We derive finite temperature expansions for relativistic fermion systems in the presence of background magnetic fields, and with nonzero chemical potential. We use the imaginary-time formalism for the finite temperature effects, the proper-time method for the background field effects, and zeta function regularization for developing the expansions. We emphasize the essential difference between even and odd dimensions, focusing on 2+1 and 3+1 dimensions. We concentrate on the high temperature limit, but we also discuss the {ital T}=0 limit with nonzero chemical potential. Copyright {copyright} 1996 Academic Press, Inc.

Two-dimensional gauge theoretic supergravities☆

Abstract We investigate two-dimensional supergravity theories, which can be built from a topological and gauge invariant action defined on an ordinary surface. One is the N = 1 supersymmetric extension of the Jackiw-Teitelboim model presented by Chamseddine in a superspace formalism. We complement the proof of Montano, Aoaki and Sonnenschein that this extension is topological and gauge invariant, based on the graded de Sitter algebra. Not only do the equations of motion correspond to the supergravity ones and do gauge transformations encompass local supersymmetries, but we also identify the ∫〈 η , F 〉-theory with the superfield formalism action written by Chamseddine. Next, we show that the N = 1 supersymmetric extension of string-inspired two-dimensional dilaton gravity put forward by Park and Strominger cannot be written as a ∫〈 η , F 〉-theory. As an alternative, we propose two topological and gauge theories that are based on a graded extension of the extended Poincare algebra and satisfy a vanishing-curvature condition. Both models are supersymmetric extensions of the string-inspired dilaton gravity.

Self-dual Chern-Simons solitons in (2+1)-dimensional Einstein gravity.

We consider a generalization of the Abelian Higgs model in curved space, by adding a Chern-Simons term. The static equations are self-dual provided we choose a suitable potential. The solutions give a self-dual Maxwell-Chern-Simons soliton that possesses a mass and a spin.