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We show how the discrete symmetries $Z_2$ and $Z_3$ combined with the superposition principle result in the $SL(2, {bf C})$-symmetry of quantum states. The role of Paulis exclusion principle in the derivation of the SL(2, C) symmetry is put forward as the source of the macroscopically observed Lorentz symmetry, then it is generalized for the case of the Z3 grading replacing the usual Z2 grading, leading to ternary commutation relations. We discuss the cubic and ternary generalizations of Grassmann algebra. Invariant cubic forms are introduced, and their symmetry group is shown to be the $SL(2,C)$ group The wave equation generalizing the Dirac operator to the Z3-graded case is constructed. Its diagonalization leads to a sixth-order equation. The solutions cannot propagate because their exponents always contain non-oscillating real damping factor. We show how certain cubic products can propagate nevertheless. The model suggests the origin of the color SU(3) symmetry.
The wave equation generalizing the Dirac operator to the Z3-graded case is introduced, whose diagonalization leads to a sixth-order equation. It intertwines not only quark and anti-quark state as well as the u and d quarks, but also the three colors,
We propose and work out a reduced density matrix functional theory (RDMFT) for calculating energies of eigenstates of interacting many-electron systems beyond the ground state. Various obstacles which historically have doomed such an approach to be u
Exceptionally clear images of intramolecular structure can be attained in dynamic force microscopy through the combination of a passivated tip apex and operation in what has become known as the Pauli exclusion regime of the tip-sample interaction. We
We define a general notion of centrally $Gamma$-graded sets and groups and of their graded products, and prove some basic results about the corresponding categories: most importantly, they form braided monoidal categories. Here, $Gamma$ is an arbitra
The traditional celestial navigation system (CNS) is used the moon, stars, and planets as celestial guides. Then the star tracker (i.e. track one star or planet or angle between it) and star sensor (i.e. sense many star simultaneous) be used to deter