314 research outputs found
Tensor-Scalar Torsion
A theory of gravity with torsion is examined in which the torsion tensor is
constructed from the exterior derivative of an antisymmetric rank two potential
plus the dual of the gradient of a scalar field. Field equations for the theory
are derived by demanding that the action be stationary under variations with
respect to the metric, the antisymmetric potential, and the scalar field. A
material action is introduced and the equations of motion are derived. The
correct conservation law for rotational angular momentum plus spin is observed
to hold in this theory.Comment: 10 pages, LaTeX, Mod. Phys. Lett. A accepte
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
Quantum Field Theory with Null-Fronted Metrics
There is a large class of classical null-fronted metrics in which a free
scalar field has an infinite number of conservation laws. In particular, if the
scalar field is quantized, the number of particles is conserved. However, with
more general null-fronted metrics, field quantization cannot be interpreted in
terms of particle creation and annihilation operators, and the physical meaning
of the theory becomes obscure.Comment: 11 page
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.
Lagrangian approach to a symplectic formalism for singular systems
We develop a Lagrangian approach for constructing a symplectic structure for
singular systems. It gives a simple and unified framework for understanding the
origin of the pathologies that appear in the Dirac-Bergmann formalism, and
offers a more general approach for a symplectic formalism, even when there is
no Hamiltonian in a canonical sense. We can thus overcome the usual limitations
of the canonical quantization, and perform an algebraically consistent
quantization for a more general set of Lagrangian systems.Comment: 30 page
The Canonical Approach to Quantum Gravity: General Ideas and Geometrodynamics
We give an introduction to the canonical formalism of Einstein's theory of
general relativity. This then serves as the starting point for one approach to
quantum gravity called quantum geometrodynamics. The main features and
applications of this approach are briefly summarized.Comment: 21 pages, 6 figures. Contribution to E. Seiler and I.-O. Stamatescu
(editors): `Approaches To Fundamental Physics -- An Assessment Of Current
Theoretical Ideas' (Springer Verlag, to appear
Quantization with maximally degenerate Poisson brackets: The harmonic oscillator!
Nambu's construction of multi-linear brackets for super-integrable systems
can be thought of as degenerate Poisson brackets with a maximal set of Casimirs
in their kernel. By introducing privileged coordinates in phase space these
degenerate Poisson brackets are brought to the form of Heisenberg's equations.
We propose a definition for constructing quantum operators for classical
functions which enables us to turn the maximally degenerate Poisson brackets
into operators. They pose a set of eigenvalue problems for a new state vector.
The requirement of the single valuedness of this eigenfunction leads to
quantization. The example of the harmonic oscillator is used to illustrate this
general procedure for quantizing a class of maximally super-integrable systems
Action functionals of single scalar fields and arbitrary--weight gravitational constraints that generate a genuine Lie algebra
We discuss the issue initiated by Kucha\v{r} {\it et al}, of replacing the
usual Hamiltonian constraint by alternative combinations of the gravitational
constraints (scalar densities of arbitrary weight), whose Poisson brackets
strongly vanish and cast the standard constraint-system for vacuum gravity into
a form that generates a true Lie algebra. It is shown that any such
combination---that satisfies certain reality conditions---may be derived from
an action principle involving a single scalar field and a single Lagrange
multiplier with a non--derivative coupling to gravity.Comment: 26 pages, plain TE
Duality properties of Gorringe-Leach equations
In the category of motions preserving the angular momentum's direction,
Gorringe and Leach exhibited two classes of differential equations having
elliptical orbits. After enlarging slightly these classes, we show that they
are related by a duality correspondence of the Arnold-Vassiliev type. The
specific associated conserved quantities (Laplace-Runge-Lenz vector and
Fradkin-Jauch-Hill tensor) are then dual reflections one of the othe
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