1,876 research outputs found
Gravitational Constraint Combinations Generate a Lie Algebra
We find a first--order partial differential equation whose solutions are all
ultralocal scalar combinations of gravitational constraints with Abelian
Poisson brackets between themselves. This is a generalisation of the Kucha\v{r}
idea of finding alternative constraints for canonical gravity. The new scalars
may be used in place of the hamiltonian constraint of general relativity and,
together with the usual momentum constraints, replace the Dirac algebra for
pure gravity with a true Lie algebra: the semidirect product of the Abelian
algebra of the new constraint combinations with the algebra of spatial
diffeomorphisms.Comment: 10 pages, latex, submitted to Classical and Quantum Gravity. Section
3 is expanded and an additional solution provided, minor errors correcte
Dirac Quantization of Two-Dimensional Dilaton Gravity Minimally Coupled to N Massless Scalar Fields
It is shown that the Callan-Giddings-Harvey-Strominger theory on the cylinder
can be consistently quantized (using Dirac's approach) without imposing any
constraints on the sign of the gravitational coupling constant or the sign (or
value) of the cosmological constant. The quantum constraints in terms of the
original geometrical variables are also derived
Canonical Equivalence of a Generic 2D Dilaton Gravity Model and a Bosonic String Theory
We show that a canonical tranformation converts, up to a boundary term, a
generic 2d dilaton gravity model into a bosonic string theory with a
Minkowskian target space.Comment: LaTeX file, 9 pages, no figure
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
Minisuperspace Model for Revised Canonical Quantum Gravity
We present a reformulation of the canonical quantization of gravity, as
referred to the minisuperspace; the new approach is based on fixing a Gaussian
(or synchronous) reference frame and then quantizing the system via the
reconstruction of a suitable constraint; then the quantum dynamics is re-stated
in a generic coordinates system and it becomes dependent on the lapse function.
The analysis follows a parallelism with the case of the non-relativistic
particle and leads to the minisuperspace implementation of the so-called {\em
kinematical action} as proposed in \cite{M02} (here almost coinciding also with
the approach presented in \cite{KT91}). The new constraint leads to a
Schr\"odinger equation for the system. i.e. to non-vanishing eigenvalues for
the super-Hamiltonian operator; the physical interpretation of this feature
relies on the appearance of a ``dust fluid'' (non-positive definite) energy
density, i.e. a kind of ``materialization'' of the reference frame. As an
example of minisuperspace model, we consider a Bianchi type IX Universe, for
which some dynamical implications of the revised canonical quantum gravity are
discussed. We also show how, on the classical limit, the presence of the dust
fluid can have relevant cosmological issues. Finally we upgrade our analysis by
its extension to the generic cosmological solution, which is performed in the
so-called long-wavelength approximation. In fact, near the Big-Bang, we can
neglect the spatial gradients of the dynamical variables and arrive to
implement, in each space point, the same minisuperspace paradigm valid for the
Bianchi IX model.Comment: 16 pages, no figures, to appear on International Journal of Modern
Physics
Quanta Without Quantization
The dimensional properties of fields in classical general relativity lead to
a tangent tower structure which gives rise directly to quantum mechanical and
quantum field theory structures without quantization. We derive all of the
fundamental elements of quantum mechanics from the tangent tower structure,
including fundamental commutation relations, a Hilbert space of pure and mixed
states, measurable expectation values, Schroedinger time evolution, collapse of
a state and the probability interpretation. The most central elements of string
theory also follow, including an operator valued mode expansion like that in
string theory as well as the Virasoro algebra with central charges.Comment: 8 pages, Latex, Honorable Mention 1997 GRG Essa
Terms of geometric action of rotating ball follower
The operation of a new rotating ball follower is presented. The influence of the values of the selected geometrical parameters of the rotating ball follower by simulation are analyzed. The ranges of value of these parameters ensuring correct operation of the rotating ball follower are defined. The operation of the rotating ball follower in real conditions are verified
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