GUT theories from Calabi-Yau 4-folds with SO(10) Singularities

We consider an SO(10) GUT model from F-theory compactified on an elliptically fibered Calabi-Yau with a D5 singularity. To obtain the matter curves and the Yukawa couplings, we use a global description to resolve the singularity. We identify the vector and spinor matter representations and their Yukawa couplings and we explicitly build the G-fluxes in the global model and check the agreement with the semi-local results. As our bundle is of type SU(2k), some extra conditions need to be applied to match the fluxes.Comment: 27 page

Two-sided estimates of minimum-error distinguishability of mixed quantum states via generalized Holevo-Curlander bounds

We prove a concise factor-of-2 estimate for the failure rate of optimally distinguishing an arbitrary ensemble of mixed quantum states, generalizing work of Holevo [Theor. Probab. Appl. 23, 411 (1978)] and Curlander [Ph.D. Thesis, MIT, 1979]. A modification to the minimal principle of Cocha and Poor [Proceedings of the 6th International Conference on Quantum Communication, Measurement, and Computing (Rinton, Princeton, NJ, 2003)] is used to derive a suboptimal measurement which has an error rate within a factor of 2 of the optimal by construction. This measurement is quadratically weighted and has appeared as the first iterate of a sequence of measurements proposed by Jezek et al. [Phys. Rev. A 65, 060301 (2002)]. Unlike the so-called pretty good measurement, it coincides with Holevo's asymptotically optimal measurement in the case of nonequiprobable pure states. A quadratically weighted version of the measurement bound by Barnum and Knill [J. Math. Phys. 43, 2097 (2002)] is proven. Bounds on the distinguishability of syndromes in the sense of Schumacher and Westmoreland [Phys. Rev. A 56, 131 (1997)] appear as a corollary. An appendix relates our bounds to the trace-Jensen inequality.Comment: It was not realized at the time of publication that the lower bound of Theorem 10 has a simple generalization using matrix monotonicity (See [J. Math. Phys. 50, 062102]). Furthermore, this generalization is a trivial variation of a previously-obtained bound of Ogawa and Nagaoka [IEEE Trans. Inf. Theory 45, 2486-2489 (1999)], which had been overlooked by the autho

New Path Equations in Absolute Parallelism Geometry

The Bazanski approach, for deriving the geodesic equations in Riemannian geometry, is generalized in the absolute parallelism geometry. As a consequence of this generalization three path equations are obtained. A striking feature in the derived equations is the appearance of a torsion term with a numerical coefficients that jumps by a step of one half from equation to another. This is tempting to speculate that the paths in absolute parallelism geometry might admit a quantum feature.Comment: 4 pages Latex file Journal Reference: Astrophysics and space science 228, 273, (1995

Deformations of the Boson sp(4,R)sp(4,R) Representation and its Subalgebras

The boson representation of the sp(4,R) algebra and two distinct deformations of it, are considered, as well as the compact and noncompact subalgebras of each. The initial as well as the deformed representations act in the same Fock space. One of the deformed representation is based on the standard q-deformation of the boson creation and annihilation operators. The subalgebras of sp(4,R) (compact u(2) and three representations of the noncompact u(1,1) are also deformed and are contained in this deformed algebra. They are reducible in the action spaces of sp(4,R) and decompose into irreducible representations. The other deformed representation, is realized by means of a transformation of the q-deformed bosons into q-tensors (spinor-like) with respect to the standard deformed su(2). All of its generators are deformed and have expressions in terms of tensor products of spinor-like operators. In this case, an other deformation of su(2) appears in a natural way as a subalgebra and can be interpreted as a deformation of the angular momentum algebra so(3). Its representation is reducible and decomposes into irreducible ones that yields a complete description of the same

Analytical Formulation of the Local Density of States around a Vortex Core in Unconventional Superconductors

On the basis of the quasiclassical theory of superconductivity, we obtain a formula for the local density of states (LDOS) around a vortex core of superconductors with anisotropic pair-potential and Fermi surface in arbitrary directions of magnetic fields. Earlier results on the LDOS of d-wave superconductors and NbSe$_2$ are naturally interpreted within our theory geometrically; the region with high intensity of the LDOS observed in numerical calculations turns out to the enveloping curve of the trajectory of Andreev bound states. We discuss experimental results on YNi$_2$B$_2$C within the quasiclassical theory of superconductivity.Comment: 13 pages, 16 figure

Isomorphisms between Quantum Group Covariant q-Oscillator Systems Defined for q and 1/q

It is shown that there exists an isomorphism between q-oscillator systems covariant under $SU_q(n)$ and $SU_{q^{-1}}(n)$. By the isomorphism, the defining relations of $SU_{q^{-1}}(n)$ covariant q-oscillator system are transmuted into those of $SU_q(n)$. It is also shown that the similar isomorphism exists for the system of q-oscillators covariant under the quantum supergroup $SU_q(n/m)$. Furthermore the cases of q-deformed Lie (super)algebras constructed from covariant q-oscillator systems are considered. The isomorphisms between q-deformed Lie (super)algebras can not obtained by the direct generalization of the one for covariant q-oscillator systems.Comment: LaTeX 13pages, RCNP-07

The Affine-Metric Quantum Gravity with Extra Local Symmetries

We discuss the role of additional local symmetries related to the transformations of connection fields in the affine-metric theory of gravity. The corresponding BRST transformations connected with all symmetries (general coordinate, local Lorentz and extra) are constructed. It is shown, that extra symmetries give the additional contribution to effective action which is proportional to the corresponding Nielsen-Kallosh ghost one. Some arguments are given, that there is no anomaly associated with extra local symmetries.Comment: 14 pages in LATEX (The version of paper accepted for publication in Class. Quant. Grav.

q-Supersymmetric Generalization of von Neumann's Theorem

Assuming that there exist operators which form an irreducible representation of the q-superoscillator algebra, it is proved that any two such representations are equivalent, related by a uniquely determined superunitary transformation. This provides with a q-supersymmetric generalization of the well-known uniqueness theorem of von Neumann for any finite number of degrees of freedom.Comment: 10 pages, Latex, HU-TFT-93-2

Nonadditivity effects in classical capacities of quantum multiple-access channels

We study classical capacities of quantum multi-access channels in geometric terms revealing breaking of additivity of Holevo-like capacity. This effect is purely quantum since, as one points out, any classical multi-access channels have their regions additive. The observed non-additivity in quantum version presented here seems to be the first effect of this type with no additional resources like side classical or quantum information (or entanglement) involved. The simplicity of quantum channels involved resembles butterfly effect in case of classical channel with two senders and two receivers.Comment: 5 pages, 5 figure

q-Analogue of Am−1⊕An−1⊂Amn−1A_{m-1}\oplus A_{n-1}\subset A_{mn-1}

A natural embedding $A_{m-1}\oplus A_{n-1}\subset A_{mn-1}$ for the corresponding quantum algebras is constructed through the appropriate comultiplication on the generators of each of the $A_{m-1}$ and $A_{n-1}$ algebras. The above embedding is proved in their $q$-boson realization by means of the isomorphism between the $\mathcal{A}_q^{-}$ (mn)$\sim {\otimes} ^n \mathcal{A}_q^{-}$(m)$\sim {\otimes}^m\mathcal{A}_q^{-}$(n) algebras.Comment: 11 pages, no figures. In memory of professor R. P. Rousse