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We figure out the explicit expression for the trace of the field equations associated to generic higher derivative theories of gravity endowed with Lagrangians depending upon the metric and its Riemann tensor, together with arbitrary order…
We develop the method of vector-fields to further study Dispersive Wave Equations. Radial vector fields are used to get a-priori estimates such as the Morawetz estimate on solutions of Dispersive Wave Equations. A key to such estimates is…
We extend the definition of Lagrangian local bias proposed by Matsubara (2008) to include curvature and higher-derivative bias operators. Evolution of initially biased tracers using perturbation theory (PT) generates multivariate bias…
We consider a classical field theory whose equations of motion follow from the least action principle, but the class of admissible trajectories is restricted by differential equations. The key element of the proposed construction is the…
We consider the application of the theory of symmetries of coupled ordinary differential equations to the case of reparametrisation invariant Lagrangians quadratic in the velocities; such Lagrangians encompass all minisuperspace models. We…
A new formulation for collisional kinetic theory is presented based on the use of Lie-transform methods to eliminate fast orbital time scales from a general bilinear collision operator. As an application of this new formalism, a general…
The effective Lagrangian and power counting rules for non-relativistic gauge theories are derived via an expansion in $1/c$. It is shown that the $1/c$ expansion leads to an effective field theory which incorporates a multipole expansion.…
A matrix method is formulated in a Lagrangian representation for the solution of the characteristic value problem governing modes of oscillation and instability in a collisionless stellar system. The underlying perturbation equations govern…
We develop a Liouville perturbation theory for weakly driven and weakly open quantum systems in situations when the unperturbed system has a number of conservations laws. If the perturbation violates the conservation laws, it drives the…
We describe a new method to parameterise dark energy theories including massive gravity, elastic dark energy and tensor-metric theories. We first examine a framework to describe any second order Lagrangian which depends on the variation of…
The Lie-point symmetry method is used to find some closed-form solutions for a constitutive equation modeling stress in elastic materials. The partial differential equation (PDE), which involves a power law with arbitrary exponent n, was…
We demonstrate electron magnetic linear dichroism as a quantitative probe of vectorial magnetic order parameters with nanometer resolution in transmission electron microscopy. Explicit inclusion of vectorial core-level exchange splitting…
The gyrokinetic paradigm in the long wavelength regime is reviewed from the perspective of variational averaging (VA). The VA-method represents a third pillar for averaging kinetic equations with highly-oscillatory characteristics, besides…
The Lagrangian formalism for tensor fields over differentiable manifolds with contravariant and covariant affine connections (whose components differ not only by sign) and metrics [$(\bar{L}_n,g)$-spaces] is considered. The functional…
The non perturbative guiding center transformation is extended to the relativistic regime and takes into account electromagnetic fluctuations. The main solutions are obtained in covariant form: the gyrating particle and the guiding particle…
A Noether-enhanced Legendre transformation from Lagrange densities to energy-momentum tensors is developed into an alternative framework for formulating classical field equations. This approach offers direct access to the Hamiltonian while…
The evolution equations of Einstein's theory and of Maxwell's theory---the latter used as a simple model to illustrate the former--- are written in gauge covariant first order symmetric hyperbolic form with only physically natural…
A new perspective on the classical mechanical formulation of particle trajectories in lorentz-violating theories is presented. Using the extended hamiltonian formalism, a Legendre Transformation between the associated covariant Lagrangian…
An integrated approach to Lie derivatives of spinors, spinor connections and the gravitational field is presented, in the context of a previously proposed, partly original formulation of a theory of Einstein-Carta-Maxwell-Dirac fields based…
The purpose of the article is to derive equations that determine the trajectory of a non-conservative natural system in configuration space in non-stationary external fields. A theorem on the change in the kinetic energy of the system is…