Related papers: Invariant conserved currents for gravity
In this paper, we make a close comparison of a covariant definition of an energy/entropy in general relativity, recently proposed by a collaboration including the present authors, with existing definitions of energies such as the one from…
The equations of Lagrangian, ideal, one-dimensional (1D), compressible gas dynamics are written in a multi-symplectic form using the Lagrangian mass coordinate $m$ and time $t$ as independent variables, and in which the Eulerian position of…
The time dependent-integrals of motion, linear in position and momentum operators, of a quantum system are extracted from Noether's theorem prescription by means of special time-dependent variations of coordinates. For the stationary case…
Noether's theorem, that local gauge variations of gauge invariant actions are identically conserved (more tautologically, that gauge variations of gauge invariants vanish) was established a century ago. Its converse, in the geometric…
We derive the Noether currents and charges associated with an internal galilean invariance---a symmetry recently postulated in the context of so-called galileon theories. Along the way we clarify the physical interpretation of the Noether…
A variational principle for gauge theories of gravity is presented, which maintains manifest covariance under the symmetries to which the action is invariant, throughout the calculation of the equations of motion and conservation laws. This…
We present the Lagrangian whose corresponding action is the trace K action for General Relativity. Although this Lagrangian is second order in the derivatives, it has no second order time derivatives and its behaviour at space infinity in…
Motivated by recent discussions of fractons, we explore nonrelativistic field theories with a continuous global symmetry, whose charge is a spatial vector. We present several such symmetries and demonstrate them in concrete examples. They…
The complete charge-current density and field strength of an arbitrarily accelerated relativistic point-charge are explicitly calculated. The current density includes, apart from the well-established three-dimensional delta-function which…
For a large class of scalar-tensor-like modified gravity whose action contains nonminimal couplings between a scalar field $\phi(x^\alpha)$ and generic curvature invariants $\mathcal{R}$ beyond the Ricci scalar $R=R^\alpha_{\;\;\alpha}$, we…
The Lagrangian, multi-dimensional, ideal, compressible gasdynamic equations are written in a multi-symplectic form, in which the Lagrangian fluid labels, $m^i$ (the Lagrangian mass coordinates) and time $t$ are the independent variables,…
We develop the covariant phase space formulation of Weyl-transverse gravity (WTG) in the presence of general timelike and spacelike boundaries. WTG is classically equivalent to General Relativity (GR) but possesses a reduced gauge symmetry…
Double field theory is an approach for massless modes of string theory, unifying and geometrizing all gauge invariance in manifest $\mathbf{O}(D,D)$ covariant manner. In this approach, we derive off-shell conserved Noether current and…
We present an E7(7) invariant Lagrangian that leads to the equations of motion of d=4 N=8 supergravity without using Lagrange multipliers. The superinvariance of this new action and the closure of the supersymmetry algebra are proved…
New features of the generalized symmetries of generic two-dimensional dilaton models of gravity are presented and invariant gravity-matter couplings are introduced. We show that there is a continuum set of Noether symmetries, which contains…
The principles of energy, symmetry, entropy, and causality conservation are discussed in a "Tetrahedron Model" of a conceptually complete "T.O.E.:" "The charges of matter are the symmetry debts of light" (Noether's Theorem). Symmetry debts…
This paper is devoted to the study of mechanical systems subjected to external forces in the framework of symplectic geometry. We obtain a Noether's theorem for Lagrangian systems with external forces, among other results regarding…
We construct the consistent ghost-free covariant scalar-vector-tensor gravity theories with second order equations of motion with derivative interactions. We impose locality, unitarity, Lorentz invariance and pseudo-Riemannian geometry as…
A Lagrangian depending on geometric variables (metric, affine connection, gauge group generators) is given which maintains compatibility with General Relativity. It generates the dynamics for Electromagnetism and other Gauge Fields along…
If the presence of a gravitational field breaks the Lorentz symmetry valid for special relativity, an "absolute motion" might be detectable. We summarize a scalar theory of gravity with a such "ether", which starts from a tentative…