Local Differential Geometry as a Representation of the SUSY Oscillator

This work proposes a natural extension of the Bargmann-Fock representation to a SUSY system. The main objective is to show that all essential structures of the n-dimensional SUSY oscillator are supplied by basic differential geometrical notions on an analytical R^n, except for the scalar product which is the only additional ingredient. The restriction to real numbers implies only a minor loss of structure but makes the essential features clearer. In particular, euclidean evolution is enforced naturally by identification with the 1-parametric group of dilations.Comment: 10 pages, late

A Generalization of the Bargmann-Fock Representation to Supersymmetry by Holomorphic Differential Geometry

In the Bargmann-Fock representation the coordinates $z^i$ act as bosonic creation operators while the partial derivatives $\partial_{z^j}$ act as annihilation operators on holomorphic $0$-forms as states of a $D$-dimensional bosonic oscillator. Considering also $p$-forms and further geometrical objects as the exterior derivative and Lie derivatives on a holomorphic ${\bf C}^D$, we end up with an analogous representation for the $D$-dimensional supersymmetric oscillator. In particular, the supersymmetry multiplet structure of the Hilbert space corresponds to the cohomology of the exterior derivative. In addition, a 1-complex parameter group emerges naturally and contains both time evolution and a homotopy related to cohomology. Emphasis is on calculus.Comment: 11 pages, LaTe

Intertwining operator for AG2AG_2 Calogero-Moser-Sutherland system

We consider generalised Calogero-Moser-Sutherland quantum Hamiltonian $H$ associated with a configuration of vectors $AG_2$ on the plane which is a union of $A_2$ and $G_2$ root systems. The Hamiltonian $H$ depends on one parameter. We find an intertwining operator between $H$ and the Calogero-Moser-Sutherland Hamiltonian for the root system $G_2$. This gives a quantum integral for $H$ of order 6 in an explicit form thus establishing integrability of $H$.Comment: 24 page

Currents on Grassmann algebras

We define currents on a Grassmann algebra $Gr(N)$ with $N$ generators as distributions on its exterior algebra (using the symmetric wedge product). We interpret the currents in terms of ${\Z}_2$-graded Hochschild cohomology and closed currents in terms of cyclic cocycles (they are particular multilinear forms on $Gr(N)$). An explicit construction of the vector space of closed currents of degree $p$ on $Gr(N)$ is given by using Berezin integration.Comment: 20 pages, CPT-93/P.2935 and ENSLAPP-440/9

Serum Uric Acid as a Marker of Coronary Calcification in Patients with Asymptomatic Coronary Artery Disease with Preserved Left Ventricular Pump Function

Objective. To evaluate the interrelation between serum uric acid and artery calcification in asymptomatic coronary artery disease subjects. Design and Methods. 126 subjects with previously documented asymptomatic coronary artery disease were enrolled in the study. Results. Mean value of serum uric acid level was 23.84 mmol/L (95% confidence interval (CI)  =  15.75–31.25 mmol/L). In multivariate Cox regression analysis, the results showed that serum uric acid levels (odds ratio , 95% CI = 1.20–1.82; ), osteopontin (, 95% CI = 1.12–1.25; ), osteoprotegerin (, 95% CI  =  1.20–1.89; ), type 2 diabetes mellitus (, 95% CI  =  1.20–1.72; ), and total cholesterol (, 95% CI = 1.10–1.22; ) were factors that independently associated with coronary artery calcification. The Cox models suggested that high quartile of serum uric acid level is very significant in predicting Agatston score index. In conclusion, we suggested that high quartile of serum uric acid level (cutoff point equaled 35.9 mmol/L) was a very significant predictor of coronary calcification examined by Agatston score index in subjects with asymptomatic coronary artery disease

Single State Supermultiplet in 1+1 Dimensions

We consider multiplet shortening for BPS solitons in N=1 two-dimensional models. Examples of the single-state multiplets were established previously in N=1 Landau-Ginzburg models. The shortening comes at a price of loosing the fermion parity $(-1)^F$ due to boundary effects. This implies the disappearance of the boson-fermion classification resulting in abnormal statistics. We discuss an appropriate index that counts such short multiplets. A broad class of hybrid models which extend the Landau-Ginzburg models to include a nonflat metric on the target space is considered. Our index turns out to be related to the index of the Dirac operator on the soliton reduced moduli space (the moduli space is reduced by factoring out the translational modulus). The index vanishes in most cases implying the absence of shortening. In particular, it vanishes when there are only two critical points on the compact target space and the reduced moduli space has nonvanishing dimension. We also generalize the anomaly in the central charge to take into account the target space metric.Comment: LaTex, 42 pages, no figures. Contribution to the Michael Marinov Memorial Volume, ``Multiple facets of quantization and supersymmetry'' (eds. M.Olshanetsky and A. Vainshtein, to be publish by World Scientific). The paper is drastically revised compared to the first version. We add sections treating the following issues: (i) a new index counting one-state supermultiplets; (ii) analysis of hybrid models of general type; (iii) generalization of the anomaly in the central charge accounting for the target space metri

Phase transitions in spinor quantum gravity on a lattice

We construct a well-defined lattice-regularized quantum theory formulated in terms of fundamental fermion and gauge fields, the same type of degrees of freedom as in the Standard Model. The theory is explicitly invariant under local Lorentz transformations and, in the continuum limit, under diffeomorphisms. It is suitable for describing large nonperturbative and fast-varying fluctuations of metrics. Although the quantum curved space turns out to be on the average flat and smooth owing to the non-compressibility of the fundamental fermions, the low-energy Einstein limit is not automatic: one needs to ensure that composite metrics fluctuations propagate to long distances as compared to the lattice spacing. One way to guarantee this is to stay at a phase transition. We develop a lattice mean field method and find that the theory typically has several phases in the space of the dimensionless coupling constants, separated by the second order phase transition surface. For example, there is a phase with a spontaneous breaking of chiral symmetry. The effective low-energy Lagrangian for the ensuing Goldstone field is explicitly diffeomorphism-invariant. We expect that the Einstein gravitation is achieved at the phase transition. A bonus is that the cosmological constant is probably automatically zero.Comment: 37 pages, 12 figures Discussion of dimensions and of the Berezinsky--Kosterlitz--Thouless phase adde