Related papers: General Relativity and Quantum Mechanics: Towards …
The Schrodinger equation for non-relativistic quantum systems is derived from some classical physics axioms within an ensemble hamiltonian framework. Such an approach enables one to understand the structure of the equation, in particular…
Different aspects of relativity, mainly in a canonical formulation, relevant for the question "Is spacetime nothing more than a mathematical space (which describes the evolution in time of the ordinary three-dimensional world) or is it a…
Wyman's less known static and spherically symmetric solution of the Einstein-Klein-Gordon equations and its recent generalization for positive cosmological constant are discussed, showing that they contain central naked singularities. By…
A generalization of the Wigner function for the case of a free particle with the ``relativistic'' Hamiltonian $\sqrt{{\bf p}^2+m^2}$ is given.
It is shown that the Schrodinger equation is a byproduct of more deterministic Boltzmann-like equation. All physical information is derived from the solution of this equation, which is a function of space and momentum. The additional terms…
We demonstrate a systematic method for solving the Hamilton-Jacobi equation for general relativity with the inclusion of matter fields. The generating functional is expanded in a series of spatial gradients. Each term is manifestly…
The regularization of a new problem, namely the three-body problem, using 'similar' coordinate system is proposed. For this purpose we use the relation of 'similarity', which has been introduced as an equivalence relation in a previous…
We consider the quantum version of Arnold's generalisation of a rigid body in classical mechanics. Thus, we quantise the motion on an arbitrary Lie group manifold of a particle whose classical trajectories correspond to the geodesics of any…
A quantum gravity theory which becomes renormalizable at short distances due to a spontaneous symmetry breaking of Lorentz invariance and diffeomorphism invariance is studied. A breaking of Lorentz invariance with the breaking patterns…
In this paper two things are done. First it is shown how a four dimensional gauged Wess-Zumino-Witten term arises from the five dimensional Einstein-Hilbert plus Gauss-Bonnet lagrangian with a special choice of the coefficients. Second, the…
We review an attempt to set a suitable foundational principle for consistent quantization of gravity based on the canonical formulation. It requires extending the spacetime description of the relativistic postulates to also encompass an…
Earlier, we had presented \cite{heuristic} heuristic arguments to show that a {\em natural unification} of the ideas of the quantum theory and those underlying the general principle of relativity is achievable by way of the measure theory…
We give an explicit form for the Lorentzian vertices recently introduced for possibly defining the dynamics of loop quantum gravity. As a result of so doing, a natural regularization of the vertices is suggested. The regularized vertices…
Given a spatially dependent mass distribution we obtain potential functions for exactly solvable nonrelativistic problems. The energy spectrum of the bound states and their wavefunctions are written down explicitly. This is accomplished by…
We treat space and time as bona fide quantum degrees of freedom on an equal footing in Hilbert space. Motivated by considerations in quantum gravity, we focus on a paradigm dealing with linear, first-order Hamiltonian and momentum…
The framework of a theory of gravity from the quantum to the classical regime is presented. The paradigm shift from full spacetime covariance to spatial diffeomorphism invariance, together with clean decomposition of the canonical…
In this continuation paper, we apply the general relativistic quantum theory for one particle systems, derived in paper II of this series, to a simple problem: the quantum Schwartzchild problem, where one particle of mass {\it m% }…
The speculation that gravity is the key to solving the quantum measurement problem has been alive for decades, without any convincing demonstration of a solution. One necessary factor in the relevant proposals is that the gravitational…
The most general version of a renormalizable $d=4$ theory corresponding to a dimensionless higher-derivative scalar field model in curved spacetime is explored. The classical action of the theory contains $12$ independent functions, which…
We obtain a new exact equilibrium solution to the N-body problem in a one-dimensional relativistic self-gravitating system. It corresponds to an expanding/contracting spacetime of a circle with N bodies at equal proper separations from one…