Related papers: Covariant Time Derivatives for Dynamical Systems
We formulate the time variation of the gravitational coupling constant in all dimensions. We show that the time variation of the gravitational coupling constant is related to the time variation of the Newton's constant in three-space…
We give in this paper which is the fifth in a series of eight a theory of covariant derivatives of multivector and extensor fields based on the geometric calculus of an arbitrary smooth manifold M, and the notion of a connection extensor…
We discuss the formulation of classical field theoretical models on $n$-dimensional noncommutative space-time defined by a generic associative star product. A simple procedure for deriving conservation laws is presented and applied to field…
In this manuscript, a conformally invariant theory of gravitation in the context of metric measure space is studied. The proposed action is invariant under both diffeomorphism and conformal transformations. Using the variational method, a…
Beginning with the principle that a closed mechanical composite system is timeless, time can be defined by the regular changes in a suitable position coordinate (clock) in the observing part, when one part of the closed composite observes…
Power laws in time and frequency appear in fields such as linear viscoelasticity and acoustics, viscous boundary layer problems, and dielectrics. This is consistent with fractional derivatives in the fundamental descriptions, since power…
In biological and engineering systems, structure, function and dynamics are highly coupled. Such interactions can be naturally and compactly captured via tensor based state space dynamic representations. However, such representations are…
Energy momentum tensors of higher-derivative free scalar conformal field theories in flat spacetime are discussed. Two algorithms for the computation of energy momentum tensors are described, which accomplish different goals: the first is…
We consider defining time as a function of a cyclical field, an abstraction of a clock. The definition of time corresponds to a novel interpretation of the relationship between space-time coordinates of observers at different locations in…
A consistent classical and quantum relativistic mechanics can be constructed if Einstein's covariant time is considered as a dynamical variable. The evolution of a system is then parametrized by a universal invariant identified with…
We derive the interaction of fermions with a dynamical space-time based on the postulate that the description of physics should be independent of the reference frame, which means to require the form-invariance of the fermion action under…
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 compare the known in literature, explicitly covariant 4-dimensional formula for the symmetric energy-momentum tensor of electromagnetic field in a medium and the energy-momentum tensor derived by Abraham in the 3-dimensional vector form.…
The theory of spaces with different (not only by sign) contravariant and covariant affine connections and metrics [}$(\bar{L}_n,g)$\QTR{it}{-spaces] is worked out within the framework of the tensor analysis over differentiable manifolds and…
The transverse-momentum-dependent distributions (TMDs), which are defined by gauge-invariant 3D parton correlators with staple-shaped lightlike Wilson lines, can be calculated from quark and gluon correlators fixed in the Coulomb gauge on a…
Our investigation of differential conservation laws in Lagrangian field theory is based on the first variational formula which provides the canonical decomposition of the Lie derivative of a Lagrangian density by a projectable vector field…
The aim of this paper is to present the main geometrical objects on the dual 1-jet bundle $J^{1*}(\cal{T},M)$ (this is the polymomentum phase space of the De Donder-Weyl covariant Hamiltonian formulation of field theory) that characterize…
A variational formulation for the geodesic circles in two-dimensional Riemannian manifold is discovered. Some relations with the uniform relativistic acceleration and the one-dimensional 'spin'-curvature interaction is investigated.
In this paper after recalling some essential tools concerning the theory of differential forms in the Cartan, Hodge and Clifford bundles over a Riemannian or Riemann-Cartan space or a Lorentzian or Riemann-Cartan spacetime we solve with…
The quantum-mechanical state vector is not directly observable even though it is the fundamental variable that appears in Schrodinger's equation. In conventional time-dependent perturbation theory, the state vector must be calculated before…