Related papers: Mathematical Clarification of General Relativistic…
We state a unified geometrical version of the variational principles for second-order classical field theories. The standard Lagrangian and Hamiltonian variational principles and the corresponding field equations are recovered from this…
The purpose of this article is to draw attention to some fundamental issues in General Relativity. It is argued that these deep issues cannot be resolved within the standard approach to general relativity that considers {\em every} solution…
We review in simple terms the covariant approaches to the canonical formulation of classical relativistic field theories (in particular gauge field theories and general relativity) and we discuss the relationships between these approaches…
The present article introduces a generalization of the (multisymplectic) Hamiltonian field theory for a Lagrangian density, allowing the formulation of this kind of field theories for variational problem of more general nature than those…
A general variational principle of classical fields with a Lagrangian containing the field quantity and its derivatives of up to the N-th order is presented. Noether's theorem is derived. The generalized Hamilton-Jacobi's equation for the…
We develop a mathematical theory of quantization of multidimensional variational principles, and compare it with traditional constructions of quantum field theory. We conjecture that mathematical realization of quantum field theory axioms,…
The first part of this article develops a variational formulation for relativistic mechanics. The results are established through standard tools of variational analysis and differential geometry. The novelty here is that the main motion…
The aim of the paper is to develop a proper mathematical formalism which can help to clarify the necessary conceptual plugins to the special principle of relativity and leads to a deeper understanding of the principle in its widest…
A variational principle is introduced to provide a new formulation and resolution for several boundary value problems with a variational structure. This principle allows one to deal with problems well beyond the weakly compact structure. As…
In this essay, I wish to share a novel perspective based on the principle of universalization in arriving at the relativistic and quantum world from the classical world. I also delve on some insightful discussion on going ``beyond''.
The problem of formulating synchronous variational principles in the context of General Relativity is discussed. Based on the analogy with classical relativistic particle dynamics, the existence of variational principles is pointed out in…
Based on the principle of causality, I advance a new principle of variation and try to use it as the most general principle for research into laws of nature.
The aim of this article is to promote the use of probabilistic methods in the study of problems in mathematical general relativity. Two new and simple singularity theorems, whose features are different from the classical singularity…
A theoretical scheme, based on a probabilistic generalization of the Hamilton's principle, is elaborated to obtain an unified description of more general dynamical behaviors determined both from a lagrangian function and by mechanisms not…
Augmented variational principles are introduced in order to provide a definition of relative conservation laws. As it is physically reasonable, relative conservation laws define in turn relative conserved quantities which measure, for…
This article develops a variational formulation for the relativistic Klein-Gordon equation. The main results are obtained through an extension of the classical mechanics approach to a more general context, which in some sense, includes the…
The purpose of this paper is to come up with a framework that "converts" existing concepts from configuration space to ordinary one. This is done by modeling our universe as a big "computer" that simulates configuration space. If that…
We postulate the applicability of the general form-invariance principle in special relativity. It is shown that this principle holds in classical mechanics. Some examples of transformations between the reference frames which satisfy this…
A recently proposed variational approach for general relativity where, in addition to the metric tensor, two independent affine connections enter the action as dynamical variables, is revised. Field equations always reduce to the Einstein…
The causality principle for the Relativistic Theory of Gravitation (RTG) is presented. It is a straightforward consequence of the RTG basic postulates. The necessary conditions for physical solutions of the gravitational field equations to…