The closest tensors of higher symmetry classes are derived in explicit form for a given elasticity tensor of arbitrary symmetry. The mathematical problem is to minimize the elastic length or distance between the given tensor and the closest elasticity tensor of the specified symmetry. Solutions are presented for three distance functions, with particular attention to the Riemannian and log-Eucli...

An algorithm is given for bringing the equations of monomial first integrals of arbitrary degree of the geodesic motion in a Riemannian space Vn into the form (FA) k = ∑ B ΓkABFB . The FA are the components of a Killing tensor Ki1...ir of arbitrary rank r and its symmetrized covariant derivatives. Explicit formulas are given for rank 1,2 and 3. Killing tensor equations in structural form allow ...

In this work we introduce the Killing-Yano symmetry on the phase space and we investigate the symplectic structure on the space of Killing-Yano tensors. We perform the detailed analyze of the ndimensional flat space and the Riemaniann manifolds with constant scalar curvature. We investigate the form of some multipole tensors, which arise in the expansion of a system of charges and currents, in ...

We construct the tensor hierarchies of generic, bosonic, 5and 6-dimensional field theories. The construction of the tensor hierarchy starts with the introduction of two tensors: the embedding tensor θ which tells us which vector is used for gauging and another tensor Z which tells us which vector is eaten by a 2-form. In dimensions d ≥ 5 these two (deformation) tensors are in principle unrelate...

The qft++ package is a library of C++ classes that facilitate numerical (not algebraic) quantum field theory calculations. Mathematical objects such as matrices, tensors, Dirac spinors, polarization and orbital angular momentum tensors, etc. are represented as C++ objects in qft++. The package permits construction of code which closely resembles quantum field theory expressions, allowing for qu...