Related papers: Arbitrary p-form Galileons
As is well known, in order for the Einstein--Hilbert action to have a well defined variation, and therefore to be used for deriving field equation through the stationary action principle, it has to be amended by the addition of a suitable…
A Siegel-type chiral p-form action is proposed in D=2(p+1) spacetime dimensions. The approach we adopt is to realize the symmetric second-rank Lagrange-multiplier field, introduced in Siegel's action, in terms of a normalized multiplication…
This paper is aimed at a (mostly) pedagogical exposition of the derivation of the motion equations of certain modifications of general relativity. Here we derive in all detail the motion equations in the Brans-Dicke theory with the cubic…
An action principle of singular hypersurfaces in general relativity and scalar-tensor type theories of gravity in the Einstein frame is presented without assuming any symmetry. The action principle is manifestly doubly covariant in the…
By generalizing the auxiliary field term in the Lagrangian of simplicial chiral models on a (d-1)-dimensional simplex, the generalized simplicial chiral models has been introduced in \c{Ali}. These models can be solved analytically only in…
An affine factorable surface of the second kind in the three dimensional pseudo-Galilean space G13 is studied depending on the invariant theory and theory of differential equation. The first and second fundamental forms, Gaussian curvature…
The fourth derivative models for two dimensional gravity are shown to be equivalent to the special version of the nonlinear sigma models coupled to 2d quantum gravity. The reduction consists in the introduction of the auxiliary scalar…
Traditionally, covariant scalar field theory models are either super renormalizable, strictly renormalizable, or nonrenormalizable. The goal of `Mixed Models' is to make sense of sums of these distinct examples, e.g.,…
We propose an equivalent formula for the higher-order derivatives used in the study of Generalized Almost Perfect Nonlinear functions over an arbitrary finite field of characteristic $p$. The result is obtained by counting the number of…
Generalizations of GL(n) abelian Toda and $\widetilde{GL}(n)$ abelian affine Toda field theories to the noncommutative plane are constructed. Our proposal relies on the noncommutative extension of a zero-curvature condition satisfied by…
We review the construction of Lagrangians for higher spin fields of mixed symmetry in the framework of graded geometry. The main advantage of the graded formalism in this context is that it provides universal expressions, in the sense that…
The maximally complicated arbitrary-dimensional "maximal" Galileon field equations simplify dramatically for symmetric configurations. Thus, spherical symmetry reduces the equations from the D- to the two-dimensional Monge-Ampere equation,…
We construct a class of interacting $(d-2)$-form theories in $d$ dimensions that are `third way' consistent. This refers to the fact that the interaction terms in the $p$-form field equations of motion neither come from the variation of an…
Sen's action for a $p$-form gauge field with self-dual field strength coupled to a spacetime metric $g$ involves an explicit Minkowski metric and the presence of this raises questions as to whether the action is coordinate independent and…
We construct differential geometry (connection, curvature, etc.) based on generalized derivations of an algebra ${\cal A}$. Such a derivation, introduced by Bresar in 1991, is given by a linear mapping $u: {\cal A} \rightarrow {\cal A}$…
An algebra A with a generalized H-action is a generalization of an H-module algebra where H is just an associative algebra with 1 and a relaxed compatibility condition between the multiplication in A and the H-action on A holds. At first…
We derive the 1-loop effective action of the cubic Galileon coupled to quantum-gravitational fluctuations in a background and gauge-independent manner, employing the covariant framework of DeWitt and Vilkovisky. Although the bare action…
We study induced additive actions on projective hypersurfaces, i.e. regular actions of the algebraic group $\mathbb G_a^m$ with an open orbit that can be extended to a regular action on the ambient projective space. We prove that if a…
We establish a correspondence between general relativity with diffeomorphism invariance and scalar field theories with Galilean invariance: notions such as the Levi-Civita connection and the Riemann tensor have a Galilean counterpart. This…
We discuss the issue initiated by Kucha\v{r} {\it et al}, of replacing the usual Hamiltonian constraint by alternative combinations of the gravitational constraints (scalar densities of arbitrary weight), whose Poisson brackets strongly…