Related papers: First Order formulation of Unimodular Gravity
The variant of electrogravitational unification has been studied on base of principle of relativity of charges and masses.
We construct the Lagrangeans of N=3 and N=4 two-form supergravities. The two-form gravity theories are classically equivalent to the Einstein gravity theories and can be formulated as gauge theories. The gauge algebras used here can be…
We present an alternative formulation of generalized unimodular gravity (GUMG), a class of modifications to general relativity characterized by a special partial breaking of general coordinate covariance. The action for this formulation is…
Based on the gauge invariant variables proposed in our previous paper [K. Nakamura, Prog. Theor. Phys. vol.110 (2003), 723.], some formulae of the perturbative curvatures of each order are derived. We follow the general framework of the…
There exist two variants of the old minimal formulation for ${\cal N}=1$ supergravity in four dimensions, in which one or each of the two auxiliary scalars is replaced by the field strength of a gauge three-form. These theories are known as…
The present article is devoted to the construction of a unified formalism for Palatini and unimodular gravity. The basic idea is to employ a relationship between unified formalism for a Griffiths variational problem and its classical…
Let $U(G)$ be a maximal unipotent subgroup of one of classical groups $G=GL(V),O(V),Sp(V)$. Let $W$ be a direct sum of copies of $V$ and its dual $V*$. For the natural action $U(G):W$, we describe a minimal system of homogeneous generators…
The Euler-Lagrange equations for some class of gravitational actions are calculated by means of Palatini principle. Polynomial structures with Einstein metrics appear among extremals of this variational problem.
We are able to derive the equations of motion for forced mechanical systems in a purely variational setting, both in the context of Lagrangian or Hamiltonian mechanics, by duplicating the variables of the system as introduced by Galley…
In this comment on arXiv:2308.07360 it is pointed out that though the authors raise an important question on the prevailing presentations of the unimodular gravity their own presentation is incomplete as well as confusing equating…
We shall review conformal gravity as a gauge natural theory and discuss the consequences of Weyl covariance on the definition of physical states.
We study two general approaches how to describe spin one particles, using vector and antisymmetric tensor fields within RChT. In this paper we focus on the question of an equivalence of both ways. The appearing problems lead us to the…
The Eulerian and Lagrangian second-order perturbation theories are solved explicitly in closed forms in $\Omega \neq 1$ and $\Lambda \neq 0$ {}Friedmann-Lema\^{\i}tre models. I explicitly write the second-order theories in terms of closed…
The wave function in the quantum theory of the O(N) extended supersymmetric particle model describes a massless free field with spin N/2. This quantum theory is here exactly solved in terms of gauge fields in arbitrary even dimensions using…
The quantum charged rigid membrane model, which is a higher derivative theory has been considered to explore its gauge symmetries using a recently developed first order formalism \cite{BMP}. Hamiltonian analysis has been performed and the…
We present a systematic theoretical framework for investigating first-order electromagnetic (EM) perturbations induced by gravitational waves (GWs). Beginning with the covariant Maxwell equations, we derive the complete first-order…
As in the case of the other gauge field theories, there is so called ``gauge'' also in general relativity. This ``gauge'' is unphysical degree of freedom. There are two kinds of ``gauges'' in general relativity. These are called the first-…
The fourth order Weyl gravity theory of Mannheim and Kazanas is based on replacing the Einstein-Hilbert action with the square of the Weyl tensor, and on modifying the matter action of the standard model of particle physics to make it…
Recently a new approach in constructing the conserved charges in cosmological Einstein's gravity was given. In this new formulation, instead of using the explicit form of the field equations a covariantly conserved rank four tensor was…
A general scheme of constructing scalar-tensor equivalents to modified gravitational actions are studied using the algebra of exterior differential forms and the first order formalism that allows an independent connection and coframe. By…