Related papers: Explicit gauge covariant Euler-Lagrange equation
We extend the Einstein-aether theory to include the Maxwell field in a nontrivial manner by taking into account its interaction with the time-like unit vector field characterizing the aether. We also include a generic matter term. We…
Fractional mechanics describes both conservative and non-conservative systems. The fractional variational principles gained importance in studying the fractional mechanics and several versions are proposed. In classical mechanics the…
We formulate higher derivative gravity with Lagrange multiplier constraint and scalar projectors. Its gauge-fixed formulation as well as vector fields formulation is developed and corresponding spontaneous Lorentz symmetry breaking is…
General covariant expressions for measurable angles, distances, velocities, and accelerations are provided in terms of fundamental parameters that can be applied in any setup. The relativistic aberration of light relationship is presented…
The simplest variant of gauge gravitation theory in Riemann-Cartan spacetime leading to the solution of the problem of cosmological singularity and dark energy problem is investigated. It is shown that this theory by certain restrictions on…
Fractional variational approach has gained much attention in recent years. There are famous fractional derivatives such as Caputo derivative, Riesz derivative and Riemann-Liouville derivative. Several versions of fractional variational…
Gauge theory underpins the quantum field theories of the standard model, and in a previous paper was shown via a geometric approach to describe classical electromagnetism in a form which approximates QED. Here we formalize and generalize…
Employing a phase space which includes the (Riemann-Liouville) fractional derivative of curves evolving on real space, we develop a restricted variational principle for Lagrangian systems yielding the so-called restricted fractional…
The choice of a star product realization for noncommutative field theory can be regarded as a gauge choice in the space of all equivalent star products. With the goal of having a gauge invariant treatment, we develop tools, such as…
As an alternative to the covariant Ostrogradski method, we show that higher-derivative relativistic Lagrangian field theories can be reduced to second differential-order by writing them directly as covariant two-derivative theories…
The relativistic Lagrangian in presence of potentials was formulated directly from the metric, with the classical Lagrangian shown embedded within it. Using it we formulated covariant equations of motion, a deformed Euler-Lagrange equation,…
In this paper, we discuss a gravitational theory based on the generalized gauge field. Our Lagrangian is invariant not only under local Lorentz transformation and the ordinary gauge transformation but also under a new gauge transformation.…
In this paper I shall consider field theories in a space of four-dimensions which have field variables consisting of the components of a metric tensor and scalar field. The field equations of these scalar-tensor field theories will be…
Let $(M,g)$ be a Riemannian manifold, and $m$ be a second metric on $M$. We give expressions of $m$'s associated connection, and Riemann curvature tensor $R_m$, in terms of $R_g$ and certain combinations of covariant derivatives of $m$…
The Einstein theory of general relativity provides a peculiar example of classical field theory ruled by non-linear partial differential equations. A number of supplementary conditions (more frequently called gauge conditions) have also…
An expression for the curvature of the "covariant" determinant line bundle is given in even dimensional space-time. The usefulness is guaranteed by its prediction of the covariant anomaly and Schwinger term. It allows a parallel derivation…
In this paper we show how the covariant gauge invariant equations for the evolution of scalar, vector and tensor perturbations for a generic $f(R)$-gravity theory can be recast in order to exploit the power of dynamical system methodology.…
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…
Grid-based discretizations of the time dependent Schr\"odinger equation coupled to an external magnetic field are converted to manifest gauge invariant discretizations. This is done using generalizations of ideas used in classical lattice…
Recently, we have demonstrated that there exists a possible relationship between q-deformed algebras in two different contexts of Statistical Mechanics, namely, the Tsallis' framework and the Kaniadakis' scenario, with a local form of…