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SO(10) group theory for the unified model building

The complete tables of Clebsch–Gordan (CG) coefficients for a wide class of SO(10) SUSY grand unified theories (GUTs) are given. Explicit expressions of states of all corresponding multiplets under…
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General formulation for proton decay rate in minimal supersymmetric SO(10) GUT

Abstract.We give an explicit formula for the proton decay rate in the minimal renormalizable supersymmetric (SUSY) SO(10) model. In this model, the Higgs fields consist of the 10 and…
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New realizations of Lie algebra kappa-deformed Euclidean space

We study Lie algebra κ-deformed Euclidean space with undeformed rotation algebra SOa(n) and commuting vectorlike derivatives. Infinitely many realizations in terms of commuting coordinates are…
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κ-Minkowski spacetime and the star product realizations

We investigate a Lie algebra-type κ-deformed Minkowski spacetime with undeformed Lorentz algebra and mutually commutative vector-like Dirac derivatives. There are infinitely many realizations of…
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κ-Poincaré–Hopf algebra and Hopf algebroid structure of phase space from twist

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Representations of non-commutative quantum mechanics and symmetries

Abstract.We present a unified approach to representations of quantum mechanics on non-commutative spaces with general constant commutators of the phase-space variables. We find two phases and duality…
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Scalar field theory on noncommutative Snyder spacetime

We construct a scalar field theory on the Snyder noncommutative space-time. The symmetry underlying the Snyder geometry is deformed at the co-algebraic level only, while its Poincare algebra is…
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Covariant realizations of kappa-deformed space

We study a Lie algebra type κ-deformed space with an undeformed rotation algebra and commutative vector-like Dirac derivatives in a covariant way. The space deformation depends on an arbitrary…
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Modification of Heisenberg uncertainty relations in noncommutative Snyder space-time geometry

We show that the Euclidean Snyder noncommutative space implies infinitely many different physical predictions. The distinct frameworks are specified by generalized uncertainty relations underlying…
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Harmonic oscillator with minimal length uncertainty relations and ladder operators

We construct creation and annihilation operators for harmonic oscillators with minimal length uncertainty relations. We discuss a possible generalization to a large class of deformations of…
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