The fact is used that electromagnetic fields are covariant (antisymmetric) tensors or
contravariant (antisymmetric) tensor densities, which are mutual conjugated. The
conjugation allows many-fold specific differentiation of the fields and leads to field
chains. An integral operation, named the generation, is considered, which is reverse to
the specific differentiation. The double generation yields zero as well as the double
differentiation. The Helmholtz decomposition is compared with the Poincare decomposition,
and many ways of the Helmholtz decomposition are presented. Laplace operator and the
inverse Laplace operator are expressed in terms of the differential and integral operations.
All results are illustrated by simple examples.
Category: Classical Physics
The growing interest in a thorough revision of the tenets of
classical electrodynamics [1,2] compels us to reconsider the
torque-production mechanism presently applied to homopolar
machines founded – indistinctively – on Ampére or
Grassmann’s basis. Recent crucial experimentation 
definitively rules out the latter rationale for its physical
Category: Classical Physics
The recently published application of a diffusion equation to prediction
of distances of planets in the solar system has been identified as
a two-dimensional Coulomb problem. A different assignment of quantum
numbers in the solar system has been proposed. This method
has been applied to the moons of Jupiter on rescaling.
The special theory of relativity and general theory of relativity have three basic
shortcomings. First, the special and general theory of relativity respectively have
two basic principles, altogether have four basic principles in the interior of relativity,
these obviously do not conform to the truth uniqueness; Second, for the two basic
principles of special theory of relativity and the two basic principles of general
theory of relativity, no one is generally correct; Third, establishing the physical
theory from the mathematics principle instead of the physical principle. In this
foundation, presents the applicable scopes of special and general theory of relativity.
Points out some wrong results caused by the theory of relativity (including the Lorentz
transformation), such as the problems that the sonic speed in vacuum permanently is equal
to zero, the twin paradox that the two brothers' state of motion are quite same, and so
on. Proposes that taking law (principle) of conservation of energy as the interdisciplinary
grand unified theory to unified process all the problems related to energy in physics,
astronomy, mechanics, chemistry, biology, medicine, engineering and so on; taking the
unified variational principle for quantization in dynamic Smarandache multi-space and the
fractal method as the interdisciplinary grand unified method; and taking the "science of
conservation of energy" to replace or partially replace the theory of relativity.
Category: Relativity and Cosmology