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Register a new userTernary generalization of Paulis principle and the Z6-graded algebras
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Richard Kerner
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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.
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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, and is therefore invariant under the product group Z2 x Z2 x Z3. The solutions of this equation 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 and of the SU(2) x U(1) that arise automatically in this model, leading to the full bosonic gauge sector of the Standard Model.
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 unfeasible are overcome. First, we resort to a generalization of the Ritz variational principle to ensemble states with fixed weights. This in combination with the constrained search formalism allows us to establish a universal functional of the one-particle reduced density matrix. Second, we employ tools from convex analysis to circumvent the too involved N-representability constraints. Remarkably, this identifies Valones pioneering work on RDMFT as a special case of convex relaxation and reveals that crucial information about the excitation structure is contained in the functionals domain. Third, to determine the crucial latter object, a methodology is developed which eventually leads to a generalized exclusion principle. The corresponding linear constraints are calculated for systems of arbitrary size.
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 discuss, from an experimentalists perspective, a number of aspects of the exclusion principle which underpin this ability to achieve submolecular resolution. Our particular focus is on the origins, history, and interpretation of Paulis principle in the context of interatomic and intermolecular interactions.
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 arbitrary (generalized) ring. The case $Gamma$ = Z/2Z is studied in detail: it is related to Clifford algebras and their discrete Clifford groups (also called Salingaros Vee groups).
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 determine the attitude of the spacecraft. Pulsar navigation also be introduced to CNS. Maser is another interested celestial in radio astronomy which has strong flux density as spectral line. Now we analysis the principle of maser navigation which base on measuring Doppler shift frequency spectra and the feasibility that use the exist instrument. We give the navigation equations of maser-based navigation system and discuss the integrated navigation use maser, then give the perspective in the Milky Way and the intergalatic. Our analysis show that use one meter antenna can achieve tens of meters position accuracy which better than todays star sensor. After integrated with maser navigation, pulsar navigation and star sensor in CNS and inertial navigation system, is it not only increase the reliability and redundancy of navigation or guiding system but also can less or abolish the depend of Global Navigation Satellite System (GNSS) which include GPS, GRONSS, Galileo and BeiDou et al. Maser navigation can give the continuous position in deep space, that means we can freedom fly successfully in the Milky Way which use celestial navigation that include maser, pulsar and traditional star sensor. Maser as nature beacon in the universe will make human freely fly in the space of the Milky Way, even outer of it. That is extraordinary in the human evolution to type III of Kardashev civilizations.
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