205 research outputs found
Covariant Canonical Gauge theory of Gravitation resolves the Cosmological Constant Problem
The covariant canonical transformation theory applied to the relativistic
theory of classical matter fields in dynamic space-time yields a new (first
order) gauge field theory of gravitation. The emerging field equations embrace
a quadratic Riemann curvature term added to Einstein's linear equation. The
quadratic term facilitates a momentum field which generates a dynamic response
of space-time to its deformations relative to de Sitter geometry, and adds a
term proportional to the Planck mass squared to the cosmological constant. The
proportionality factor is given by a dimensionless parameter governing the
strength of the quadratic term. In consequence, Dark Energy emerges as a
balanced mix of three contributions, (A)dS curvature plus the residual vacuum
energy of space-time and matter. The Cosmological Constant Problem of the
Einstein-Hilbert theory is resolved as the curvature contribution relieves the
rigid relation between the cosmological constant and the vacuum energy density
of matter
Canonical Transformation Path to Gauge Theories of Gravity
In this paper, the generic part of the gauge theory of gravity is derived,
based merely on the action principle and on the general principle of
relativity. We apply the canonical transformation framework to formulate
geometrodynamics as a gauge theory. The starting point of our paper is
constituted by the general De~Donder-Weyl Hamiltonian of a system of scalar and
vector fields, which is supposed to be form-invariant under (global) Lorentz
transformations. Following the reasoning of gauge theories, the corresponding
locally form-invariant system is worked out by means of canonical
transformations. The canonical transformation approach ensures by construction
that the form of the action functional is maintained. We thus encounter amended
Hamiltonian systems which are form-invariant under arbitrary spacetime
transformations. This amended system complies with the general principle of
relativity and describes both, the dynamics of the given physical system's
fields and their coupling to those quantities which describe the dynamics of
the spacetime geometry. In this way, it is unambiguously determined how spin-0
and spin-1 fields couple to the dynamics of spacetime.
A term that describes the dynamics of the free gauge fields must finally be
added to the amended Hamiltonian, as common to all gauge theories, to allow for
a dynamic spacetime geometry. The choice of this "dynamics Hamiltonian" is
outside of the scope of gauge theory as presented in this paper. It accounts
for the remaining indefiniteness of any gauge theory of gravity and must be
chosen "by hand" on the basis of physical reasoning. The final Hamiltonian of
the gauge theory of gravity is shown to be at least quadratic in the conjugate
momenta of the gauge fields -- this is beyond the Einstein-Hilbert theory of
General Relativity.Comment: 16 page
Extended Hamilton-Lagrange formalism and its application to Feynman's path integral for relativistic quantum physics
With this paper, a consistent and comprehensive treatise on the foundations
of the extended Hamilton-Lagrange formalism will be presented. In this
formalism, the system's dynamics is parametrized along a time-like system
evolution parameter , and the physical time is treated as a dependent
variable on equal footing with all other configuration space variables
. In the action principle, the conventional classical action
is then replaced by the generalized action , with and
denoting the conventional and the extended Lagrangian, respectively. In the
existing literature, the discussion is restricted to only those extended
Lagrangians that are homogeneous forms of first order in the
velocities.
It is shown that a class of extended Lagrangians exists that are
correlated to corresponding conventional Lagrangians without being
homogeneous functions in the velocities. Then the Legendre transformation of
to an extended Hamiltonian exists. With this class of extended
Hamiltonians, an extended canonical formalism is presented that is completely
analogous to the conventional Hamiltonian formalism. The physical time and
the negative value of the conventional Hamiltonian then constitute and an
additional pair of conjugate canonical variables. The extended formalism also
includes a theory of extended canonical transformations, where the time
variable is also subject to transformation.
In the extended formalism, the system's dynamics is described as a motion on
a hypersurface within an extended phase space of even dimension. It is shown
that the hypersurface condition does not embody a constraint as the condition
is automatically satisfied on the system path that is given by the solution of
the extended set of canonical equations.Comment: 49 pages, one figur
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A model-based assessment of the effects of projected climate change on the water resources of Jordan
This paper is concerned with the quantification of the likely effect of anthropogenic climate change on the water resources of Jordan by the end of the twenty-first century. Specifically, a suite of hydrological models are used in conjunction with modelled outcomes from a regional climate model, HadRM3, and a weather generator to determine how future flows in the upper River Jordan and in the Wadi Faynan may change. The results indicate that groundwater will play an important role in the water security of the country as irrigation demands increase. Given future projections of reduced winter rainfall and increased near-surface air temperatures, the already low groundwater recharge will decrease further. Interestingly, the modelled discharge at the Wadi Faynan indicates that extreme flood flows will increase in magnitude, despite a decrease in the mean annual rainfall. Simulations projected no increase in flood magnitude in the upper River Jordan. Discussion focuses on the utility of the modelling framework, the problems of making quantitative forecasts and the implications of reduced water availability in Jordan
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