Topology at the Planck Length

A basic arbitrariness in the determination of the topology of a manifold at the Planck length is discussed. An explicit example is given of a `smooth' change in topology from the 2-sphere to the 2-torus through a sequence of noncommuting geometries. Applications are considered to the theory of D-branes within the context of the proposed $M$(atrix) theory.Comment: Orsay Preprint 97/34, 17 pages, Late

Holomorphic Quantization on the Torus and Finite Quantum Mechanics

We construct explicitly the quantization of classical linear maps of $SL(2, R)$ on toroidal phase space, of arbitrary modulus, using the holomorphic (chiral) version of the metaplectic representation. We show that Finite Quantum Mechanics (FQM) on tori of arbitrary integer discretization, is a consistent restriction of the holomorphic quantization of $SL(2, Z)$ to the subgroup $SL(2, Z)/\Gamma_l$, $\Gamma_l$ being the principal congruent subgroup mod l, on a finite dimensional Hilbert space. The generators of the ``rotation group'' mod l, $O_{l}(2)\subset SL(2,l)$, for arbitrary values of l are determined as well as their quantum mechanical eigenvalues and eigenstates.Comment: 12 pages LaTeX (needs amssymb.sty). Version as will appear in J. Phys.

Strange Attractors in Dissipative Nambu Mechanics : Classical and Quantum Aspects

We extend the framework of Nambu-Hamiltonian Mechanics to include dissipation in $R^{3}$ phase space. We demonstrate that it accommodates the phase space dynamics of low dimensional dissipative systems such as the much studied Lorenz and R\"{o}ssler Strange attractors, as well as the more recent constructions of Chen and Leipnik-Newton. The rotational, volume preserving part of the flow preserves in time a family of two intersecting surfaces, the so called {\em Nambu Hamiltonians}. They foliate the entire phase space and are, in turn, deformed in time by Dissipation which represents their irrotational part of the flow. It is given by the gradient of a scalar function and is responsible for the emergence of the Strange Attractors. Based on our recent work on Quantum Nambu Mechanics, we provide an explicit quantization of the Lorenz attractor through the introduction of Non-commutative phase space coordinates as Hermitian $N \times N$ matrices in $R^{3}$. They satisfy the commutation relations induced by one of the two Nambu Hamiltonians, the second one generating a unique time evolution. Dissipation is incorporated quantum mechanically in a self-consistent way having the correct classical limit without the introduction of external degrees of freedom. Due to its volume phase space contraction it violates the quantum commutation relations. We demonstrate that the Heisenberg-Nambu evolution equations for the Quantum Lorenz system give rise to an attracting ellipsoid in the $3 N^{2}$ dimensional phase space.Comment: 35 pages, 4 figures, LaTe

Analytic Representation of Finite Quantum Systems

A transform between functions in R and functions in Zd is used to define the analogue of number and coherent states in the context of finite d-dimensional quantum systems. The coherent states are used to define an analytic representation in terms of theta functions. All states are represented by entire functions with growth of order 2, which have exactly d zeros in each cell. The analytic function of a state is constructed from its zeros. Results about the completeness of finite sets of coherent states within a cell are derived

New Physics in CP Asymmetries and Rare B Decays

We review and update the effects of physics beyond the standard model on CP asymmetries in B decays. These asymmetries can be significantly altered if there are important new-physics contributions to \bqbqbar mixing. This same new physics will therefore also contribute to rare, flavor-changing B decays. Through a study of such decays, we show that it is possible to partially distinguish the different models of new physics.Comment: 42 pages, plain TeX (macros included), 1 figure (included). A few sentences added, references updated. Present manuscript is now identical to the version accepted for publication in Phys. Rev.

Probing the charged Higgs boson at the LHC in the CP-violating type-II 2HDM

We present a phenomenological study of a CP-violating two-Higgs-doublet Model with type-II Yukawa couplings at the Large Hadron Collider (LHC). In the light of recent LHC data, we focus on the parameter space that survives the current and past experimental constraints as well as theoretical bounds on the model. Once the phenomenological scenario is set, we analyse the scope of the LHC in exploring this model through the discovery of a charged Higgs boson produced in association with a W boson, with the former decaying into the lightest neutral Higgs and a second W state, altogether yielding a b\bar b W^+W^- signature, of which we exploit the W^+W^- semileptonic decays.Comment: 37 pages, 16 figures; v2 updated treatment of LHC constraint

Is Ankyrin a genetic risk factor for psychiatric phenotypes?

Background Genome wide association studies reported two single nucleotide polymorphisms in ANK3 (rs9804190 and rs10994336) as independent genetic risk factors for bipolar disorder. Another SNP in ANK3 (rs10761482) was associated with schizophrenia in a large European sample. Within the debate on common susceptibility genes for schizophrenia and bipolar disorder, we tried to investigate common findings by analyzing association of ANK3 with schizophrenia, bipolar disorder and unipolar depression. Methods We genotyped three single nucleotide polymorphisms (SNPs) in ANK3 (rs9804190, rs10994336, and rs10761482) in a case-control sample of German descent including 920 patients with schizophrenia, 400 with bipolar affective disorder, 220 patients with unipolar depression according to ICD 10 and 480 healthy controls. Sample was further differentiated according to Leonhard's classification featuring disease entities with specific combination of bipolar and psychotic syndromes. Results We found no association of rs9804190 and rs10994336 with bipolar disorder, unipolar depression or schizophrenia. In contrast to previous findings rs10761482 was associated with bipolar disorder (p = 0.015) but not with schizophrenia or unipolar depression. We observed no association with disease entities according to Leonhard's classification. Conclusion Our results support a specific genetic contribution of ANK3 to bipolar disorder though we failed to replicate findings for schizophrenia. We cannot confirm ANK3 as a common risk factor for different diseases

Genome-wide study of association and interaction with maternal cytomegalovirus infection suggests new schizophrenia loci.

Genetic and environmental components as well as their interaction contribute to the risk of schizophrenia, making it highly relevant to include environmental factors in genetic studies of schizophrenia. This study comprises genome-wide association (GWA) and follow-up analyses of all individuals born in Denmark since 1981 and diagnosed with schizophrenia as well as controls from the same birth cohort. Furthermore, we present the first genome-wide interaction survey of single nucleotide polymorphisms (SNPs) and maternal cytomegalovirus (CMV) infection. The GWA analysis included 888 cases and 882 controls, and the follow-up investigation of the top GWA results was performed in independent Danish (1396 cases and 1803 controls) and German-Dutch (1169 cases, 3714 controls) samples. The SNPs most strongly associated in the single-marker analysis of the combined Danish samples were rs4757144 in ARNTL (P=3.78 × 10(-6)) and rs8057927 in CDH13 (P=1.39 × 10(-5)). Both genes have previously been linked to schizophrenia or other psychiatric disorders. The strongest associated SNP in the combined analysis, including Danish and German-Dutch samples, was rs12922317 in RUNDC2A (P=9.04 × 10(-7)). A region-based analysis summarizing independent signals in segments of 100 kb identified a new region-based genome-wide significant locus overlapping the gene ZEB1 (P=7.0 × 10(-7)). This signal was replicated in the follow-up analysis (P=2.3 × 10(-2)). Significant interaction with maternal CMV infection was found for rs7902091 (P(SNP × CMV)=7.3 × 10(-7)) in CTNNA3, a gene not previously implicated in schizophrenia, stressing the importance of including environmental factors in genetic studies