We give an overview of the first integrals of motion of particles in the presence of external gauge fields in a covariant Hamiltonian approach. The special role of Stäckel–Killing and Killing–Yano tensors is pointed out. Some nontrivial examples involving Runge–Lenz type conserved quantities are explicitly worked out. A condition of the electromagnetic field to maintain the hidden symmetry of t...

We present the gauged N = 4 (half-maximal) supergravities in four and five spacetime dimensions coupled to an arbitrary number of vector multiplets. The gaugings are parameterized by a set of appropriately constrained constant tensors, which transform covariantly under the global symmetry groups SL(2) × SO(6, n) and SO(1, 1) × SO(5, n), respectively. In terms of these ten-sors the universal Lag...

A group theoretical procedure, introduced earlier in [6], to decompose bilocal light–ray operators into (harmonic) operators of definite twist is applied to the case of arbitrary 2nd rank tensors. As a generic example the bilocal gluon operator is considered which gets contributions of twist–2 up to twist–6 from four different symmetry classes characterized by corresponding Young tableaux; also...

We present a full symmetry classification of fermion matter in and out thermal equilibrium. Our approach starts from first principles, the ten different classes linear anti-linear state transformations fermionic Fock spaces, symmetries defined via invariance properties dynamical equation for density matrix. The object are then generators reversible dynamics, dissipation fluctuations featuring g...

The hybrid density functional theory is applied to calculate the electron paramagnetic resonance parameters, i.e, the gand A-tensors of some planar Cobalt(II) complexes with a C2v symmetry. Calculations were done for four systems: Co(acacen), Co(tacacen), Co(seacacen) and Co(sacsac)2. The following hybrid functionals were employed: B3LYP, B3PW91, mPW1PW91 and PBE0. The expected large deviation ...