Related papers: Covariant Derivatives of Extensor Fields
I construct combined electric and magnetic field variables which independently represent energy flows in the forward and backward directions respectively, and use these to re-formulate Maxwell's equations. The emphasis is on detailed…
The classical fields with fractional derivatives are investigated by using the fractional Lagrangian formulation.The fractional Euler-Lagrange equations were obtained and two examples were studied.
We study unitary multigraded non-associative algebras R generated by an ordered set X over a field K of characteristic 0 such that the mappings d_k: x_l->delta_{kl}, x_k,x_l in X, can be extended to derivations of R. The class of these…
We find a covariant completion of the flat-space multi-galileon theory, preserving second-order field equations. We then generalise this to arrive at an enlarged class of second order theories describing multiple scalars and a single…
We survey some important properties of fields of generalized series and of exponential-logarithmic series, with particular emphasis on their possible differential structure, based on a joint work of the author with S. Kuhlmann [KM12b,KM11].
We present a direct derivation of the typical time derivatives used in a continuum description of complex fluid flows, harnessing the principles of the kinematics of line elements. The evolution of the microstructural conformation tensor in…
Motivated by extending the functional stochastic calculus, to important functionals to which it does not apply, a notion of functional derivative along a curve is introduced. This new setting is developed by incorporating path-dependent…
The space of derivations of finite dimensional evolution algebras associated to graphs over a field with characteristic zero has been completely characterized in the literature. In this work we generalize that characterization by describing…
We develop a theory of extensions of hyperfields that generalizes the notion of field extensions. Since hyperfields have a multivalued addition, we must consider two kinds of extensions that we call weak hyperfield extensions and strong…
Gauge theories with and without matter are formulated in the derivative expansion. Amplitudues are derived as a power series in the energy scales; there are simplifications as compared with the usual loop expansion. The incorporation and…
How do we take repeated derivatives of composed multivariate functions? for one-dimensional functions, the common tools consist of the Fa\'a di Bruno formula with Bell polynomials; while there are extensions of the Fa\'a di Bruno formula,…
The model of kappa-deformed space is an interesting example of a noncommutative space, since it allows a deformed symmetry. In this paper we present new results concerning different sets of derivatives on the coordinate algebra of…
In the recent development in a various disciplines of physics, it is noted the need for including the deformed versions of the exponential functions. In this paper, we consider the deformations which have two purposes: to have them like…
Generalizations of the Hamilton-Jacobi and Schrodinger equations for multidimensional variational problems of field theory are deduced. These generalizations are so-called variational differential equations.
A simplified version of Higher Covariant Derivative regularization for Yang-Mills theory is constructed. This may make Higher Covariant Derivative method more attractive for practical calculations.
Exact relations between gauge-invariant vacuum correlators in QCD are derived. Derivatives of the correlators are expressed in terms of higher orders correlators. The behaviour of the correlators at large and small distances due to these…
Some derivation-based differential calculi which have been used to construct models of noncommutative gauge theories are presented and commented. Some comparisons between them are made.
The aim of this review is to discuss the ways to obtain results based on gravity with higher derivatives in D-dimensional world. We considered the following ways: (1) reduction to scalar tensor gravity, (2) direct solution of the equations…
In this paper we provide some conditions under which a Lie derivation on a trivial extension algebra is proper, that is, it can be decomposed into the sum of a derivation and a center valued map. We extend some known results on the…
Connections between Lie derivatives and the deviation equation has been investigated in spaces with affine connection. The deviation equations of the geodesics as well as deviation equations of non-geodesics trajectories have been obtained…