Related papers: Diffeomorphisms, Noether Charges and Canonical For…
Using a manifestly invariant Lagrangian density based on Clebsch fields and suitable for geophysical fluid dynamics, the conservation of mass, entropy, momentum and energy, and the associated symmetries are investigated. In contrast, it is…
A didactic and systematic derivation of Noether point symmetries and conserved currents is put forward in special relativistic field theories, without a priori assumptions about the transformation laws. Given the Lagrangian density, the…
We proceed to study a (1+1)-dimensional dilaton gravity system with a hyperbolic dilaton potential. Introducing a couple of new variables leads to two copies of Liouville equations with two constraint conditions. In particular, in conformal…
Quantization of two-dimensional dilaton gravity coupled to conformal matter is investigated. Working in conformal gauge about a fixed background metric, the theory may be viewed as a sigma model whose target space is parameterized by the…
Quantum theory of dilaton gravity coupled to a nonlinear sigma model with a maximally symmetric target space is studied in $2+\epsilon$ dimensions. The ultraviolet stable fixed point for the curvature of the nonlinear sigma model demands a…
General Relativity reduced to two dimensions possesses a large group of symmetries that exchange classical solutions. The associated Lie algebra is known to contain the affine Kac-Moody algebra $A_1^{(1)}$ and half of a real Witt algebra.…
A model for 2D-quantum gravity from the Virasoro symmetry is studied. The notion of space-time naturally arises as a homogeneous space associated with the kinematical (non-dynamical) SL(2,R) symmetry in the kernel of the Lie-algebra central…
The ultrarelativistic limit of twodimensional dilaton gravity is presented and its associated (anti-)selfdual energy momentum tensor is derived. It is localized on a null line, although the line element remains twice differentiable.…
We explore global Poisson-Lie (PL) symmetries using a Lagrangian, or "covariant phase space" approach, that manifestly preserves spacetime covariance. PL symmetries are the classical analog of quantum-group symmetries. In the Noetherian…
In the (2+2) formulation of general relativity spacetime is foliated by a two-parameter family of spacelike 2-surfaces (instead of the more usual one-parameter family of spacelike 3-surfaces). In a partially gauge-fixed setting (double-null…
In the framework of superfield formalism, we demonstrate the existence of a new local, covariant, continuous and nilpotent (dual-BRST) symmetry for the BRST invariant Lagrangian density of a self-interacting two ($1 + 1$)-dimensional (2D)…
In the investigation and resolution of the cosmological constant problem the inclusion of the dynamics of quantum gravity can be a crucial step. In this work we suggest that the quantum constraints in a canonical theory of gravity can…
Within the general framework of spatially covariant theories of gravity, we study the conditions for having only the two tensorial degrees of freedom. Generally, there are three degrees of freedom propagating in the theory, of which two are…
We study the 1-form diffeomorphism cohomologies within a local conformal Lagrangian Field Theory model built on a two dimensional Riemann surface with no boundary. We consider the case of scalar matter fields and the complex structure is…
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…
As a contribution towards the understanding for the field equations of diffeomorphism invariant theories of pure gravity, we demonstrate in great detail that the expression for the field equations of such theories can be derived within the…
In the literature on $f(T)$ gravity, the status of local Lorentz invariance and the number of physical degrees of freedom have been controversial issues. Relying on a detailed Hamiltonian analysis, we show that there are several scenarios…
It is well known that both the symplectic structure and the Poisson brackets of classical field theory can be constructed directly from the Lagrangian in a covariant way, without passing through the non-covariant canonical Hamiltonian…
We examine the diffeomorphisms of a symplectic vector space that preserve a chosen symplectic potential. Our examination yields an explicit description of these diffeomorphisms when the chosen potential differs from the canonical potential…
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…