相关论文: Covariant Derivatives of Extensor Fields

Expressions for the derivatives of the Legendre polynomials of the first kind with respect to the order of these polynomials are given. An explicit form for the fourth derivative is presented.

The perturbative dynamics of quantum field theories is described by a recursive expansion similar to the well known loop expansion. The equivalent formulation based on low-energy dynamics via an expansion in derivatives is well known in the…

An investigation of classical fields with fractional derivatives is presented using the fractional Hamiltonian formulation. The fractional Hamilton's equations are obtained for two classical field examples. The formulation presented and the…

We show that the difference of the extension dimensions of two derived equivalent algebras is bounded above by the minimal length of a tilting complex associated with a derived equivalence, and that the extension dimension is an invariant…

Spinor fields depending on tensor fields and other spinor fields are considered. The concept of extended spinor fields is introduced and the theory of differentiation for such fields is developed.

Estimates for invariant distances of convexifiable, $\C$-convexifiable and planar domains are given.

We study a Lie algebra type $\kappa$-deformed space with undeformed rotation algebra and commutative vector-like Dirac derivatives in a covariant way. Space deformation depends on an arbitrary vector. Infinitely many covariant realizations…

From a previous paper where we proposed a description of general relativity within the gravito-electromagnetic limit, we propose an alternative modified gravitational theory. As in the former version, we analyze the vector and tensor…

We give a first-order definition of key polynomials, we show the links with previous definitions, that it is relevant to study key degrees, and to use a kind of valuations that we call partially multiplicative. We also prove or reprove…

Expressions for the derivatives with respect to order of modified Bessel functions evaluated at integer orders and certain integral representations of associated Legendre functions with modulus argument greater than unity are used to…

It is a basic introduction to differential graded Lie algebras, Maurer-Cartan equation and associated deformation functors.

We determine the most general group of equivalence transformations for a family of differential equations defined by an arbitrary vector field on a manifold. We also find all invariants and differential invariants for this group up to the…

A field theoretical perturbation theory in inverse powers of coupling constant is developed which is manifestly covariant in every order of the expansion. A dilatation operator serves as an evolution dynamical one in a scale non-invariant…

Recently developed applications in the field of machine learning and computational physics rely on automatic differentiation techniques, that require stable and efficient linear algebra gradient computations. This technical note provides a…

We discuss the covariant formulation of local field theories described by the Companion Lagrangian associated with p-branes. The covariantisation is shown to be useful for clarifying the geometrical meaning of the field equations and also…

The n-th derivative of a tensor valued function of a tensor is defined by a finite number of coefficients each with closed form expression.

Biadjoint scalar field theories are increasingly important in the study of scattering amplitudes in various string and field theories. Recently, some first exact nonperturbative solutions of biadjoint scalar theory were presented, with a…

We obtain a complete time expansion of the pull-back operator generated by a real analytic flow of real analytic automorphisms acting on analytic tensor sections of a manifold. Our expansion is given in terms of multiple Lie derivatives.…

We have recently presented an extension of the standard variational calculus to include the presence of deformed derivatives in the Lagrangian of a system of particles and in the Lagrangian density of field-theoretic models. Classical…

In one of our former papers {\it Endomorphisms of the measure algebra of commutative hypergroups arXiv:2204.07499 we considered exponential monomials on hypergroups and higher order derivations of the corresponding measure algebra.…