Related papers: Lie - point and variational symmetries in minisupe…
We develop a new approach to find asymptotic symmetries in general relativity as a modification of the Lie-algebra-based approach proposed in T. Tomitsuka et al. [Classical Quantum Gravity 38, 225007 (2021)]. Those authors proposed an…
It might seem that a choice of a time coordinate in Hamiltonian formulations of general relativity breaks the full four-dimensional diffeomorphism covariance of the theory. This is not the case. We construct explicitly the complete set of…
The structure of a diffeomorphism invariant Lagrangians for an extended object W embedded in a bulk space M is discussed by following a close analogy with the relativistic particle in electromagnetic field as a system that is…
A variational scheme for the derivation of generalized, symmetry-induced continuity equations for Hermitian and non-Hermitian quantum mechanical systems is developed. We introduce a Lagrangian which involves two complex wave fields and…
We develop the equations of motion for full body models that describe the dynamics of rigid bodies, acting under their mutual gravity. The equations are derived using a variational approach where variations are defined on the Lie group of…
The concept of weak Lie motion (weak Lie symmetry) is introduced through ${\cal{L}}_{\xi}{\cal{L}}_{\xi}g_{ab}=0,$ (${\cal{L}}_{\xi}{\cal{L}}_{\xi}f=0$). Applications are given which exhibit a reduction of the usual symmetry, e.g., in the…
In this article we investigate whether a theory based on a classical Lagrangian for the minimal Standard-Model Extension (SME) can be quantized such that the result is equal to the corresponding low-energy Hamilton operator obtained from…
A Lagrangian formalism is used to study the motion of a spinning massive particle in Friedmann--Robertson--Walker and G\"odel spacetimes, as well as in a general Schwarzschild-like spacetime and in static spherically symmetric conformally…
Near-horizon symmetries are studied for black hole solutions to Einstein equations containing supertranslation field constructed by Compere and Long. The metric is transformed to variables in which the horizon is located at the surface…
Superpotentials offer a direct means of calculating conserved charges associated with the asymptotic symmetries of space-time. Yet superpotentials have been plagued with inconsistencies, resulting in nonphysical or incongruent values for…
The gauge symmetries of a general dynamical system can be systematically obtained following either a Hamiltonean or a Lagrangean approach. In the former case, these symmetries are generated, according to Dirac's conjecture, by the first…
Gauge symmetries lead to first-class constraints. This assertion is of course true only for non trivial gauge symmetries, i.e., gauge symmetries that act non trivially on-shell on the dynamical variables. We illustrate this well-appreciated…
Geometric mechanics is a branch of mathematical physics that studies classical mechanics of particles and fields from the point of view of geometry. In a geometric language, symmetries can be expressed in a natural manner as vector fields…
A method is presented for finding the Lie point symmetry transformations acting simultaneously on difference equations and lattices, while leaving the solution set of the corresponding difference scheme invariant. The method is applied to…
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 construct the truly minimal left-right symmetric model by utilizing only the fields dictated by supersymmetry and automatic R-parity conservation. Allowing for non-renormalizable operators in the superpotential, we show that parity can…
Through defining irreducible loop integrals (ILIs), a set of consistency conditions for the regularized (quadratically and logarithmically) divergent ILIs are obtained to maintain the generalized Ward identities of gauge invariance in…
We consider theories describing the dynamics of a four-dimensional metric, whose Lagrangian is diffeomorphism invariant and depends at most on second derivatives of the metric. Imposing degeneracy conditions we find a set of Lagrangians…
We study the Lie and Noether point symmetries of a class of systems of second-order differential equations with $n$ independent and $m$ dependent variables ($n\times m$ systems). We solve the symmetry conditions in a geometric way and…
We consider the lagrangian $L=F(R)$ in classical (=non-quantized) two-dimensional fourth-order gravity and give new relations to Einstein's theory with a non-minimally coupled scalar field. We distinguish between scale-invariant lagrangians…