Equations of motion, Noncommutativity and Quantization

We study the relation between a given set of equations of motion in configuration space and a Poisson bracket. A Poisson structure is consistent with the equations of motion if the symplectic form satisfy some consistency conditions. When the symplectic structure is commutative these conditions are the Helmholtz integrability equations for the nonrestricted inverse problem of the calculus of variations. We have found the corresponding consistency conditions for the symplectic noncommutative case.Comment: 18 pages, to appear PL

Spacetime torsion and parity violation: a gauge invariant formulation

The possibility of parity violation through spacetime torsion has been explored in a scenario containing fields with different spins. Taking the Kalb-Ramond field as the source of torsion, an explicitly parity violating $U(1)_{EM}$ gauge invariant theory has been constructed by extending the KR field with a Chern-Simons term.Comment: 4 pages, RevTe

Metric-affine gauge theory of gravity II. Exact solutions

In continuing our series on metric-affine gravity (see Gronwald IJMP D6 (1997) 263 for Part I), we review the exact solutions in this theory.Comment: Revtex file, 25 pages, final version to appear in IJMP

Lagrangian versus Quantization

We discuss examples of systems which can be quantized consistently, although they do not admit a Lagrangian description.Comment: 8 pages, no figures; small corrections, references adde

Quantization of Nonstandard Hamiltonian Systems

The quantization of classical theories that admit more than one Hamiltonian description is considered. This is done from a geometrical viewpoint, both at the quantization level (geometric quantization) and at the level of the dynamics of the quantum theory. A spin-1/2 system is taken as an example in which all the steps can be completed. It is shown that the geometry of the quantum theory imposes restrictions on the physically allowed nonstandard quantum theories.Comment: Revtex file, 23 pages, no figure

On the generalized Hamiltonian structure of 3D dynamical systems

The Poisson structures for 3D systems possessing one constant of motion can always be constructed from the solution of a linear PDE. When two constants of the motion are available the problem reduces to a quadrature and the structure functions include an arbitrary function of them

What is the Geometry of Superspace ?

We investigate certain properties of the Wheeler-DeWitt metric (for constant lapse) in canonical General Relativity associated with its non-definite nature. Contribution to the conference on Mach's principle: "From Newtons Bucket to Quantum Gravity", July 26-30 1993, Tuebingen, GermanyComment: 10 pages, Plain Te

The Husain-Kuchar Model: Time Variables and Non-degenerate Metrics

We study the Husain-Kuchar model by introducing a new action principle similar to the self-dual action used in the Ashtekar variables approach to Quantum Gravity. This new action has several interesting features; among them, the presence of a scalar time variable that allows the definition of geometric observables without adding new degrees of freedom, the appearance of a natural non-degenerate four-metric and the possibility of coupling ordinary matter.Comment: LaTeX, 22 pages, accepted for publication in Phys. Rev.

Angular Symmetry Breaking Induced by Electromagnetic Field

It is well known that velocities does not commute in presence of an electromagnetic field. This property implies that angular algebra symmetries, such as the sO(3) and Lorentz algebra symmetries, are broken. To restore these angular symmetries we show the necessity of adding the Poincare momentum M to the simple angular momentum L. These restorations performed succesively in a flat space and in a curved space lead in each cases to the generation of a Dirac magnetic monopole. In the particular case of the Lorentz algebra we consider an application of our theory to the gravitoelectromagnetism. In this last case we establish a qualitative relation giving the mass spectrum for dyons.Comment: 19 page

Variations on the Seventh Route to Relativity

As motivated in the full abstract, this paper further investigates Barbour, Foster and O Murchadha (BFO)'s 3-space formulation of GR. This is based on best-matched lapse-eliminated actions and gives rise to several theories including GR and a conformal gravity theory. We study the simplicity postulates assumed in BFO's work and how to weaken them, so as to permit the inclusion of the full set of matter fields known to occur in nature. We study the configuration spaces of gravity-matter systems upon which BFO's formulation leans. In further developments the lapse-eliminated actions used by BFO become impractical and require generalization. We circumvent many of these problems by the equivalent use of lapse-uneliminated actions, which furthermore permit us to interpret BFO's formulation within Kuchar's generally covariant hypersurface framework. This viewpoint provides alternative reasons to BFO's as to why the inclusion of bosonic fields in the 3-space approach gives rise to minimally-coupled scalar fields, electromagnetism and Yang--Mills theory. This viewpoint also permits us to quickly exhibit further GR-matter theories admitted by the 3-space formulation. In particular, we show that the spin-1/2 fermions of the theories of Dirac, Maxwell--Dirac and Yang--Mills--Dirac, all coupled to GR, are admitted by the generalized 3-space formulation we present. Thus all the known fundamental matter fields can be accommodated. This corresponds to being able to pick actions for all these theories which have less kinematics than suggested by the generally covariant hypersurface framework. For all these theories, Wheeler's thin sandwich conjecture may be posed, rendering them timeless in Barbour's sense.Comment: Revtex version; Journal-ref adde