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We show in a new way that the general relativity action (and Lagrangian)in recent Einstein-Palatini formulation is equivalent in four dimensions to the action (and Lagrangian) of a gauge field. This paper is a continuation of the previous…
I consider theories of gravity built not just from the metric and affine connection, but also other (possibly higher rank) symmetric tensor(s). The Lagrangian densities are scalars built from them, and the volume forms are related to…
The aim of the present article is to give physical meaning to the ingredients of standard gauge field theory in the framework of the scale relativity theory. Owing to the principle of the relativity of scales, the scale-space is not…
We give a variational formulation of General Relativity, with coupling to a cosmological constant, to scalar fields, to vector fields and to spinor fields (all with possible mass and interaction terms). Among the matter fields, we include…
Self-similar models are important in general relativity and other fundamental theories. In this paper we shall discuss the ``similarity hypothesis'', which asserts that under a variety of physical circumstances solutions of these theories…
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…
We formulate a theory of shape valid for objects of arbitrary dimension whose contours are path connected. We apply this theory to the design and modeling of viable trajectories of complex dynamical systems. Infinite families of…
We investigate the problem of finding a pure spin-connection formulation of General Relativity with non-vanishing cosmological constant. We first revisit the problem at the linearised level and find that the pure spin-connection, quadratic…
We discuss the problem of consistent description of higher spin massive fields coupled to external gravity. As an example we consider massive field of spin 2 in arbitrary gravitational field. Consistency requires the theory to have the same…
How to make compatible both boundary and gauge conditions for generally covariant theories using the gauge symmetry generated by first class constraints is studied. This approach employs finite gauge transformations in contrast with…
We consider static, spherically symmetric vacuum solutions to the equations of a theory of gravity with the Lagrangian f(R) where R is the scalar curvature and f is an arbitrary function. Using a well-known conformal transformation, the…
The purely affine, metric-affine and purely metric formulation of general relativity are dynamically equivalent and the relation between them is analogous to the Legendre relation between the Lagrangian and Hamiltonian dynamics. We show…
We develop a covariant variational framework for relativistic electromagnetic continua (fluids and solid) based on Hamilton's principle formulated directly in the material description. The approach extends the geometric theory of…
The aim of this paper is to discuss a kinematical algebraic structure of a theory of gravity, that would be unitary, renormalizable and coupled in the same manner to both spinorial and tensorial matter fields. An analysis of the common…
These lectures present an elementary introduction to quantum gauge fields. The first aim is to show how, in the tree approximation, gauge invariance follows from covariance and unitarity. This leads to the standard construction of the…
We introduce in the framework of the linear approximation of General relativity a natural distinction between General gauge transformations generated by any vector field and those Special ones for which this vector field is a gradient. This…
Gauge field theories may quite generally be defined as describing the coupling of a matter-field to an interaction-field, and they are suitably represented in the mathematical framework of fiber bundles. Their underlying principle is the…
We present a novel theory of gravity by considering an extension of symmetric teleparallel gravity. This is done by introducing, in the framework of the metric-affine formalism, a new class of theories where the nonmetricity $Q$ is…
In my lectures I will deal with three seemingly unrelated problems: i) to what extent is general relativity exceptional among metric gravity theories? ii) is it possible to define gravitational energy density applying field-theory approach…
A new approach to the dynamics of the universe based on work by O Murchadha, Foster, Anderson and the author is presented. The only kinematics presupposed is the spatial geometry needed to define configuration spaces in purely relational…