Related papers: An improved Noether's theorem for spacetime symmet…

Diffeomorphisms and an internal symmetry (e.g., local Lorentz invariance) are typically regarded as the symmetries of any geometrical gravity theory, including general relativity. In the first-order formalism, diffeomorphisms can be thought…

We consider the issue of correspondence between symmetries and conserved quantities in the class of linear relativistic higher-derivative theories of derived type. In this class of models the wave operator is a polynomial in another…

Gravitation might make a preferred frame appear, and with it a clear space/time separation--the latter being, a priori, needed by quantum mechanics (QM) in curved space-time. Several models of gravitation with an ether are discussed: they…

We give a version of Noether theorem adapted to the framework of mu-symmetries; this extends to such case recent work by Muriel, Romero and Olver in the framework of lambda-symmetries, and connects mu-symmetries of a Lagrangian to a…

We revisit the old problem of the energy-momentum tensor in general relativistic field theories. On the basis of the general covariance we derive a simple equation for the Hilbert and Noether energy-momentum tensors for the scalar and…

We study supersymmetric extension of the Einstein-aether gravitational model where local Lorentz invariance is broken down to the subgroup of spatial rotations by a vacuum expectation value of a timelike vector field called aether.…

We approach higher-order variational problems of Herglotz type from an optimal control point of view. Using optimal control theory, we derive a generalized Euler-Lagrange equation, transversality conditions, a DuBois-Reymond necessary…

We address the consequences of invariance properties of the free energy of spatially inhomogeneous quantum many-body systems. We consider a specific position-dependent transformation of the system that consists of a spatial deformation and…

In this paper we use Noether symmetries of the geodesic Lagrangian in Bianchi V spacetimes to study various cosmological solutions of Einstein's field equations. Our first result is the identification of the subalgebras of Noether…

It is well known that the Noether symmetry approach proves to be very useful not only to fix physically viable cosmological models but also to reduce dynamics and achieve exact solutions. In this work, We examine a formal framework of…

We reexamine the energy-momentum tensor in classical electrodynamics from the perspective of spacetime-dependent translations, i.e., diffeomorphism invariance in flat spacetime. When energy-momentum is identified through local translations…

This article examines the analytic solutions of isotropic spacetime with the minimal coupling of scalar field and matter in the context of energy-momentum squared gravity. The scalar field includes quintessence and phantom dark energy…

Explicit expressions are constructed for a locally conserved vector current associated with a continuous internal symmetry and for energy-momentum and angular-momentum density tensors associated with the Poincar\'e group in field theories…

Recent research has highlighted the non-uniqueness problem of energy-momentum tensors in linearized gravity; many different tensors are published in the literature, yet for particular calculations a unique expression is required. It has…

We discuss general properties of the conservation law associated with a local symmetry. Using Noether's theorem and a generalized Belinfante symmetrization procedure in 3+1 dimensions, a symmetric energy-momentum (pseudo) tensor for the…

We look into the general aspects of space-time symmetries in presence of torsion, and how the latter is affected by such symmetries. Focusing in particular to space-times which either exhibit maximal symmetry on their own, or could be…

We analyze the cosmology of a general Scalar-Tensor theory which encompasses generalized Brans-Dicke theory, Gauss-Bonnet gravity, non-minimal derivative gravity, generalized Galileon gravity and also the general k-essence type models.…

For a field theory that is invariant under diffeomorphisms there is a subtle interplay between symmetries, conservation laws and the phase space of the theory. The natural language for describing these ideas is that of differential forms…

We embark on a systematic study of continuous non-invertible symmetries, focusing on 1+1d CFTs. We describe a generalized version of Noether's theorem, where continuous non-invertible symmetries are associated to $\textit{non-local}$…

This paper deals with the symmetry analysis of the Einstein Cartan theory which is an extension of the General Relativity and it accounts for the space-time torsion. We begin by applying Noether Theorem to the Lagrangian of the FRW type…