Related papers: Geometric Justification of the Fundamental Interac…
Special relativity beyond its basic treatment can be inaccessible, in particular because introductory physics courses typically view special relativity as decontextualized from the rest of physics. We seek to place special relativity back…
We describe a new type of gravity-matter models where gravity couples in a non-conventional way to two distinct scalar fields providing a unified Lagrangian action principle description of: (a) the evolution of both "early" and "late"…
The theory of Gravitomagnetism and spinor quantum mechanics describing the interaction between the Dirac spinor field, the electromagnetic field, and a weak gravitational field is extended by including the Lagrangian density of the free…
The Lagrangians and Hamiltonians of classical field theory require to comprise gauge fields in order to be form-invariant under local gauge transformations. These gauge fields have turned out to correctly describe pertaining elementary…
A novel approach for Lagrange formulation for field theories is proposed in terms of Kawaguchi geometry (areal metric space). On the extended configuration space M for classical field theory composed of spacetime and field configuration…
We construct a lagrangian geometric formulation for first-order field theories using the canonical structures of first-order jet bundles, which are taken as the phase spaces of the systems in consideration. First of all, we construct all…
We briefly discuss new models of an `affine' theory of gravity in multidimensional space-times with symmetric connections. We use and generalize Einstein's proposal to specify the space-time geometry by use of the Hamilton principle to…
The field-theoretical approach is reviewed. Perturbations in general relativity as well as in an arbitrary $D$-dimensional metric theory are studied on a background, which is a solution (arbitrary) of the theory. Lagrangian for…
In this work, we review a plethora of modified theories of gravity with generalized curvature-matter couplings. The explicit nonminimal couplings, for instance, between an arbitrary function of the scalar curvature $R$ and the Lagrangian…
The basic physics disciplines of Maxwell's electrodynamics and Newton's mechanics have been thoroughly tested in the laboratory, but they can nevertheless also support nonphysical solutions. The unphysical nature of some dynamical…
In this paper we first show that any coupled system consisting of a gravitational plus a free electromagnetic field can be described geometrically in the sense that both Maxwell equations and Einstein equation having as source term the…
We develop a model-independent approach to lagrangian perturbation theory for the large scale structure of the universe. We focus on the displacement field for dark matter particles, and derive its most general structure without assuming a…
We review the interactions of massive fields of arbitrary integer spins with the constant electromagnetic field and symmetrical Einstein space in the gauge invariant framework. The problem of obtaining the gauge-invariant Lagrangians of…
It is widely accepted that the fundamental geometrical law of nature should follow from an action principle. The particular subset of transformations of a system's dynamical variables that maintain the form of the action principle comprises…
We give a geometrical interpretation for the principle of stationary action in classical Lagrangian particle mechanics. In a nutshell, the difference of the action along a path and its variation effectively ``counts'' the possible…
We propose a reformulation of gravitation in which the gravitational interaction is treated as a genuine force rather than an inertial effect arising from spacetime geometry. Within this framework, the difference between the affine…
The multiplicative Lagrangian and Hamiltonian introduce an additional parameter that, despite its variation, results in identical equations of motion as those derived from the standard Lagrangian. This intriguing property becomes even more…
The issue of electric charges in interaction with partially reflective surfaces is addressed by means of field theoretic methods. It is proposed an enlarged Maxwell lagrangian, describing the electromagnetic field in the presence of a…
We consider massive half-integer higher spin fields coupled to an external constant electromagnetic field in flat space of an arbitrary dimension and construct a gauge invariant Lagrangian in the linear approximation in the external field.…
We shall here consider extended theories of gravitation in the metric-affine formalism with matter coupled directly to the connection. A sufficiently general procedure will be exhibited to solve the resulting field equation associated to…