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

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

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 $s$, and the physical time $t$ is treated as a dependent variable $t(s)$ on equal footing with all other configuration space variables $q^{i}(s)$. In the action principle, the conventional classical action $L dt$ is then replaced by the generalized action $L_{e}ds$, with $L$ and $L_{e}$ denoting the conventional and the extended Lagrangian, respectively. In the existing literature, the discussion is restricted to only those extended Lagrangians $L_{e}$ that are homogeneous forms of first order in the velocities. It is shown that a class of extended Lagrangians $L_{e}$ exists that are correlated to corresponding conventional Lagrangians $L$ without being homogeneous functions in the velocities. Then the Legendre transformation of $L_{e}$ to an extended Hamiltonian $H_{e}$ 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 $t$ 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 $t(s)$ 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