Random lattice superstrings

We propose some new simplifying ingredients for Feynman diagrams that seem necessary for random lattice formulations of superstrings. In particular, half the fermionic variables appear only in particle loops (similarly to loop momenta), reducing the supersymmetry of the constituents of the Type IIB superstring to N=1, as expected from their interpretation in the 1/N expansion as super Yang-Mills.Comment: Section 5 which describes contributions of the string measure adde

Discrete versions of some Dirac type equations and plane wave solutions

A discrete version of the plane wave solution to some discrete Dirac type equations in the spacetime algebra is established. The conditions under which a discrete analogue of the plane wave solution satisfies the discrete Hestenes equation are briefly discussed.Comment: 12 pages. arXiv admin note: text overlap with arXiv:1609.0459

Twisted Superspace for N=D=2 Super BF and Yang-Mills with Dirac-K\"ahler Fermion Mechanism

We propose a twisted D=N=2 superspace formalism. The relation between the twisted super charges including the BRST charge, vector and pseudo scalar super charges and the N=2 spinor super charges is established. We claim that this relation is essentially related with the Dirac-K\"ahler fermion mechanism. We show that a fermionic bilinear form of twisted N=2 chiral and anti-chiral superfields is equivalent to the quantized version of BF theory with the Landau type gauge fixing while a bosonic bilinear form leads to the N=2 Wess-Zumino action. We then construct a Yang-Mills action described by the twisted N=2 chiral and vector superfields, and show that the action is equivalent to the twisted version of the D=N=2 super Yang-Mills action, previously obtained from the quantized generalized topological Yang-Mills action with instanton gauge fixing.Comment: 36 page

Symplectic Dirac-K\"ahler Fields

For the description of space-time fermions, Dirac-K\"ahler fields (inhomogeneous differential forms) provide an interesting alternative to the Dirac spinor fields. In this paper we develop a similar concept within the symplectic geometry of phase-spaces. Rather than on space-time, symplectic Dirac-K\"ahler fields can be defined on the classical phase-space of any Hamiltonian system. They are equivalent to an infinite family of metaplectic spinor fields, i.e. spinors of Sp(2N), in the same way an ordinary Dirac-K\"ahler field is equivalent to a (finite) mulitplet of Dirac spinors. The results are interpreted in the framework of the gauge theory formulation of quantum mechanics which was proposed recently. An intriguing analogy is found between the lattice fermion problem (species doubling) and the problem of quantization in general.Comment: 86 pages, late

Generalized Gauge Theories and Weinberg-Salam Model with Dirac-K\"ahler Fermions

We extend previously proposed generalized gauge theory formulation of Chern-Simons type and topological Yang-Mills type actions into Yang-Mills type actions. We formulate gauge fields and Dirac-K\"ahler matter fermions by all degrees of differential forms. The simplest version of the model which includes only zero and one form gauge fields accommodated with the graded Lie algebra of $SU(2|1)$ supergroup leads Weinberg-Salam model. Thus the Weinberg-Salam model formulated by noncommutative geometry is a particular example of the present formulation.Comment: 33 pages, LaTe

Cavitation inception of a van der Waals fluid at a sack-wall obstacle

Cavitation in a liquid moving past a constraint is numerically investigated by means of a free-energy lattice Boltzmann simulation based on the van der Waals equation of state. The fluid is streamed past an obstacle and, depending on the pressure drop between inlet and outlet, vapor formation underneath the corner of the sack-wall is observed. The circumstances of cavitation formation are investigated and it is found that the local bulk pressure and mean stress are insufficient to explain the phenomenon. Results obtained in this study strongly suggest that the viscous stress, interfacial contributions to the local pressure, and the Laplace pressure are relevant to the opening of a vapor cavity. This can be described by a generalization of Joseph's criterion that includes these contributions. A macroscopic investigation measuring mass flow rate behavior and discharge coefficient was also performed. As theoretically predicted, mass flow rate increases linearly with the square root of the pressure drop. However, when cavitation occurs, the mass flow growth rate is reduced and eventually it collapses into a choked flow state. In the cavitating regime, as theoretically predicted and experimentally verified, the discharge coefficient grows with the Nurick cavitation number

Cholera hotspots and surveillance constraints contributing to recurrent epidemics in Tanzania

Objective: We described the dynamics of cholera in Tanzania between 2007 and 2017 and assessed the weaknesses of the current surveillance system in providing necessary data in achieving the global roadmap to 2030 for cholera control. Results: The Poisson-based spatial scan identifed cholera hotspots in mainland Tanzania. A zero-infated Poisson regression investigated the relationship between the incidence of cholera and available demographic, socio-economic and climatic exposure variables. Four cholera hotspots were detected covering 17 regions, home to 28 million people, including the central regions and those surrounding the Lakes Victoria, Tanganyika and Nyaza. The risk of experiencing cholera in these regions was up to 2.9 times higher than elsewhere in the country. Regression analyses revealed that every 100 km of water perimeter in a region increased the cholera incidence by 1.5%. Due to the compilation of surveillance data at regional level rather than at district, we were unable to reliably identify any other signifcant risk factors and specifc hotspots. Cholera high-risk populations in Tanzania include those living near lakes and central regions. Successful surveillance require disaggregated data available weekly and at district levels in order to serve as data for action to support the roadmap for cholera control.Published versio

A holomorphic representation of the Jacobi algebra

A representation of the Jacobi algebra $\mathfrak{h}_1\rtimes \mathfrak{su}(1,1)$ by first order differential operators with polynomial coefficients on the manifold $\mathbb{C}\times \mathcal{D}_1$ is presented. The Hilbert space of holomorphic functions on which the holomorphic first order differential operators with polynomials coefficients act is constructed.Comment: 34 pages, corrected typos in accord with the printed version and the Errata in Rev. Math. Phys. Vol. 24, No. 10 (2012) 1292001 (2 pages) DOI: 10.1142/S0129055X12920018, references update

Hypercomplex Integrable Systems

In this paper we study hypercomplex manifolds in four dimensions. Rather than using an approach based on differential forms, we develop a dual approach using vector fields. The condition on these vector fields may then be interpreted as Lax equations, exhibiting the integrability properties of such manifolds. A number of different field equations for such hypercomplex manifolds are derived, one of which is in Cauchy-Kovaleskaya form which enables a formal general solution to be given. Various other properties of the field equations and their solutions are studied, such as their symmetry properties and the associated hierarchy of conservation laws.Comment: Latex file, 19 page

A condensed matter interpretation of SM fermions and gauge fields

We present the bundle Aff(3) x C x /(R^3), with a geometric Dirac equation on it, as a three-dimensional geometric interpretation of the SM fermions. Each C x /(R^3) describes an electroweak doublet. The Dirac equation has a doubler-free staggered spatial discretization on the lattice space Aff(3) x C (Z^3). This space allows a simple physical interpretation as a phase space of a lattice of cells in R^3. We find the SM SU(3)_c x SU(2)_L x U(1)_Y action on Aff(3) x C x /(R^3) to be a maximal anomaly-free special gauge action preserving E(3) symmetry and symplectic structure, which can be constructed using two simple types of gauge-like lattice fields: Wilson gauge fields and correction terms for lattice deformations. The lattice fermion fields we propose to quantize as low energy states of a canonical quantum theory with Z_2-degenerated vacuum state. We construct anticommuting fermion operators for the resulting Z_2-valued (spin) field theory. A metric theory of gravity compatible with this model is presented too.Comment: Minimal modifications in comparison with the published versio