58 research outputs found
Algebraic analysis of a model of two-dimensional gravity
An algebraic analysis of the Hamiltonian formulation of the model
two-dimensional gravity is performed. The crucial fact is an exact coincidence
of the Poisson brackets algebra of the secondary constraints of this
Hamiltonian formulation with the SO(2,1)-algebra. The eigenvectors of the
canonical Hamiltonian are obtained and explicitly written in closed
form.Comment: 21 pages, to appear in General Relativity and Gravitatio
The Hamiltonian of Einstein affine-metric formulation of General Relativity
It is shown that the Hamiltonian of the Einstein affine-metric (first order)
formulation of General Relativity (GR) leads to a constraint structure that
allows the restoration of its unique gauge invariance, four-diffeomorphism,
without the need of any field dependent redefinition of gauge parameters as is
the case for the second order formulation. In the second order formulation of
ADM gravity the need for such a redefinition is the result of the non-canonical
change of variables [arXiv: 0809.0097]. For the first order formulation, the
necessity of such a redefinition "to correspond to diffeomorphism invariance"
(reported by Ghalati [arXiv: 0901.3344]) is just an artifact of using the
Henneaux-Teitelboim-Zanelli ansatz [Nucl. Phys. B 332 (1990) 169], which is
sensitive to the choice of linear combination of tertiary constraints. This
ansatz cannot be used as an algorithm for finding a gauge invariance, which is
a unique property of a physical system, and it should not be affected by
different choices of linear combinations of non-primary first class
constraints. The algorithm of Castellani [Ann. Phys. 143 (1982) 357] is free
from such a deficiency and it leads directly to four-diffeomorphism invariance
for first, as well as for second order Hamiltonian formulations of GR. The
distinct role of primary first class constraints, the effect of considering
different linear combinations of constraints, the canonical transformations of
phase-space variables, and their interplay are discussed in some detail for
Hamiltonians of the second and first order formulations of metric GR. The first
order formulation of Einstein-Cartan theory, which is the classical background
of Loop Quantum Gravity, is also discussed.Comment: 74 page
The Hamiltonian formulation of General Relativity: myths and reality
A conventional wisdom often perpetuated in the literature states that: (i) a
3+1 decomposition of space-time into space and time is synonymous with the
canonical treatment and this decomposition is essential for any Hamiltonian
formulation of General Relativity (GR); (ii) the canonical treatment
unavoidably breaks the symmetry between space and time in GR and the resulting
algebra of constraints is not the algebra of four-dimensional diffeomorphism;
(iii) according to some authors this algebra allows one to derive only spatial
diffeomorphism or, according to others, a specific field-dependent and
non-covariant four-dimensional diffeomorphism; (iv) the analyses of Dirac
[Proc. Roy. Soc. A 246 (1958) 333] and of ADM [Arnowitt, Deser and Misner, in
"Gravitation: An Introduction to Current Research" (1962) 227] of the canonical
structure of GR are equivalent. We provide some general reasons why these
statements should be questioned. Points (i-iii) have been shown to be incorrect
in [Kiriushcheva et al., Phys. Lett. A 372 (2008) 5101] and now we thoroughly
re-examine all steps of the Dirac Hamiltonian formulation of GR. We show that
points (i-iii) above cannot be attributed to the Dirac Hamiltonian formulation
of GR. We also demonstrate that ADM and Dirac formulations are related by a
transformation of phase-space variables from the metric to lapse
and shift functions and the three-metric , which is not canonical. This
proves that point (iv) is incorrect. Points (i-iii) are mere consequences of
using a non-canonical change of variables and are not an intrinsic property of
either the Hamilton-Dirac approach to constrained systems or Einstein's theory
itself.Comment: References are added and updated, Introduction is extended,
Subsection 3.5 is added, 83 pages; corresponds to the published versio
Sweet Sorghum Planting Effects on Stalk Yield and Sugar Quality in Semi-Arid Tropical Environment
Sweet sorghum [Sorghum bicolor (L.) Moench] has potential as a bioenergy crop for producing food, fiber, and fermentable sugar. Unlike dryland grain sorghum, little information is available on the influence of staggered planting and genotypes, especially in semiarid tropical environments. The objectives of the present study were (i) to quantify the effects of planting time and genotype on stalk and biomass yields, juice sugar quality, and (ii) to identify the most productive genotypes and planting windows for sustainable feedstock supply. Four commercial sweet sorghum genotypes (SSV84, SSV74, CSV19SS, and CSH22SS) were planted on five planting dates (1 June, 16 June, 1 July, 16 July, and 1 August) during the rainy (June–October) season of 2008 and 2009 in Hyderabad (17°27´ N, 78°28´ E), India. Planting in early and mid-June produced significantly (P ≤ 0.05) higher fresh stalk yield and grain yield than later planting dates. Commercial hybrid CSH22SS produced significantly more stalk, grain, sugar, and ethanol yield over genotypes SSV84 or SSV74. Based on the stalk yield, juice sugar quality, sugar, and ethanol yields, the optimum planting dates for sweet sorghum in semiarid tropical climate is early June to early July. Planting sweet sorghum during this time allows more feedstock to be harvested and hence extends the period for sugar mill operation by about 1 mo, that is, from the first to the last week of October
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