The quaternionic description of quantum mechanics

The associated production of a dark particle and photon, represented as a mono-γ event, is a promising channel to probe particle content and dynamics in the dark sector. In this study, we investigate the properties of the mono-γ production of vector dark matter at future colliders. Photon-like and Pauli operators as well as triple gauge boson interactions involving dark matter are considered in the framework of effective field theory. We show that, in comparison with the Pauli operator, the triple gauge boson couplings are significantly more interesting in high energy colliders. Beam polarization effects are also analyzed, and we show that the experimental sensitivities cannot be significantly enhanced because of the smaller luminosity.

The cosmic connections between physics on the very largest and very smallest scales are reviewed with an emphasis on the symbiotic relation between elementary particle physics and cosmology. After a review of the early Universe as a cosmic accelerator, various cosmological and astrophysical constraints on models of particle physics are outlined. To illustrate this approach to particle physics via cosmology, reference is made to several areas of current research: baryon non-conservation and baryon asymmetry; free quarks, heavy hadrons and other exotic relics; primordial nucleosynthesis and neutrino masses.

Relativity, noncommutative geometry, renormalization and particle physics

We are used to thinking of an operator acting once, twice, and so on. However, an operator can be analytically continued to the operator raised to a complex power. Applications include (s,r) diagrams and an extension of Fractional Calculus where commutativity of fractional derivatives is preserved, generating integrals and non-standard derivations of theorems in Number Theory, non-integer power series and breaking of Leibniz and Chain rules, pseudo-groups and symmetry deforming models in particle physics and cosmology, non-local effect in analytically continued matrix representations and its connection with noncommutative geometry, particle-physics-like scatterings of zeros of analytically continued Bernoulli polynomials, and analytic continuation of operators in QM, QFT and Strings.

The main purpose of this work is to establish the existence of a weak solution to the incompressible 2D Euler equations with initial vorticity consisting of a Radon measure with distinguished sign in H − 1, compactly supported in the closed right half-plane, superimposed on its odd reflection in the left half-plane. We make use of a new a priori estimate to control the interaction between positive and negative vorticity at the symmetry axis. We prove that a weak limit of a sequence of approximations obtained by either regularizing the initial data or by using the vanishing viscosity method is a weak solution of the incompressible 2D Euler equations. We also establish the equivalence at the level of weak solutions between mirror symmetric flows in the full plane and flows in the half-plane. Finally, we extend our existence result to odd L 1 perturbations, without distinguished sign, of our original initial vorticity.

Infinitesimal bendings of order are considered, including analytic bendings (), of an -dimensional surface in an -dimensional () space of constant curvature. It is proved that to any solution of an times formally varied system of Gauss-Codazzi-Ricci equations there corresponds an infinitesimal bending of order of the surface in . A general form is established for solutions of this system that determine infinitesimal motions of various orders. By using these results we obtain criteria for rigidity and nonrigidity of order , and also for analytic bendability and nonbendability of a class of multidimensional surfaces of codimension in flat spaces, which contains, in particular, Riemannian products of hypersurfaces.Bibliography. 13 titles.

Zeta regularization has proven to be a powerful and reliable tool for the\nregularization of the vacuum energy density in ideal situations. With the\nHadamard complement, it has been shown to provide finite (and meaningful)\nanswers too in more involved cases, as when imposing physical boundary\nconditions (BCs) in two-- and higher--dimensional surfaces (being able to\nmimic, in a very convenient way, other {\\it ad hoc} cut-offs, as non-zero\ndepths). What we have considered is the {\\it additional} contribution to the cc\ncoming from the non-trivial topology of space or from specific boundary\nconditions imposed on braneworld models (kind of cosmological Casimir effects).\nAssuming someone will be able to prove (some day) that the ground value of the\ncc is zero, as many had suspected until very recently, we will then be left\nwith this incremental value coming from the topology or BCs. We show that this\nvalue can have the correct order of magnitude in a number of quite reasonable\nmodels involving small and large compactified scales and/or brane BCs, and\nsupergravitons.\n

We describe generalizations of the Pauli group, the Clifford group and\nstabilizer states for qudits in a Hilbert space of arbitrary dimension d. We\nexamine a link with modular arithmetic, which yields an efficient way of\nrepresenting the Pauli group and the Clifford group with matrices over the\nintegers modulo d. We further show how a Clifford operation can be efficiently\ndecomposed into one and two-qudit operations. We also focus in detail on\nstandard basis expansions of stabilizer states.\n

Surface flashover across an insulator in a vacuum is a destructive plasma discharge which undermines the behaviors of a range of applications in electrical engineering, particle physics and space engineering, etc. This phenomenon is widely modeled by the particle-in-cell (PIC) simulation, here the continuum and kinetic simulation method is first proposed and implemented as an alternative solution for flashover modeling, aiming for the prevention of unfavorable particle noises in PIC models. A one dimension in space, two dimensions in velocity kinetic simulation model is constructed. Modeling setup, physical assumptions, and simulation algorithm are presented in detail, and a comparison with the well-known secondary electron (SE) emission avalanche analytical expression and existing PIC simulation are made. The obtained kinetic simulation results are consistent with the analytical prediction, and feature noise-free data of surface charge density as well as fluxes of primary and SEs. Discrepancies between the two simulation models and analytical predictions are explained. The code is convenient for updating and to include additional physical processes. The possible implementations of outgassing and plasma species for the final breakdown stage are discussed. The proposed continuum and kinetic approach are expected to inspire future modeling studies for the flashover mechanism and mitigation.

We give a review of our joint work on strict deformation of BHTZ 2+1 black holes \cite{BRS02,BDHRS03}. However some results presented here are not published elsewhere, and an effort is made for enlightening the instrinsical aspect of the constructions. This shows in particular that the three dimensional case treated here could be generalized to an anti-de Sitter space of arbitrary dimension provided one disposes of a universal deformation formula for the actions of a parabolic subgroup of its isometry group. Comment: 10 pages, based on a talk given by P.B., to appear in the proceedings of the workshop `Noncommutative Geometry and Physics 2004' (Feb. 2004, Keio University, Japan) (World Scientific)

Feed forward neural network for classification instantly requires that the modular length of input vector is 1. On the other hand, Stereographic projection can map a point in n dimensional real space into the surface of unit sphere in (n+1) dimensional real space. Because the modular length of any point in the unit sphere of (n+1) dimensional real surface is 1 and stereographic projection is a bijective mapping, Stereographic projection can be treated as an implementation for the normalization of vector in n dimensional real space. Experimental results shown that feed forward neural network can classify data instantly and accurately if stereographic projection is used to normalized input vector for feed forward network.

Classical and quantized spinor soliton are investigated from the viewpoint that the elementary particles are regarded as a kind of soliton. The non-linear spinor equation proposed by Heisenberg is studied in two-dimensional case which is usually called the Thirring model.

Chapter 17 Euclidean structure in finite dimensional normed spaces

The one-loop contribution to vacuum polarization is calculated for the adjoint fermions in three dimensional noncommutative spaces, both at zero and finite temperature. At zero temperature, we confirm a previously found result for the parity odd part and subsequently analyze the even parity part, which exhibits UV/IR mixing. We discuss in detail, two regimes of the high temperature behavior of the parity odd part. When the thermal wavelength is much smaller, as compared to the noncommutativity scale, we find an interesting Fermi-Bose transmutation in the nonplanar part.

We investigate cosmological predictions on the early universe based on the noncommutative geometry (NCG) models of gravity coupled to matter. Using the renormalization group analysis for the standard model with right-handed neutrinos and Majorana mass terms, which is the particle
\nphysics content of the most recent NCG models, we analyze the behavior of the coefficients of the gravitational and cosmological terms in the Lagrangian derived from the asymptotic expansion of the spectral action functional of NCG. We find emergent Hoyle–Narlikar and conformal
\ngravity at the see-saw scales and a running effective gravitational constant, which affects the propagation of gravitational waves and the evaporation law of primordial black holes and provides Linde models of negative gravity in the early universe. The same renormalization group
\nanalysis also governs the running of the effective cosmological constant of the model. The model also provides a Higgs-based slow-roll inflationary mechanism, for which one can explicitly compute the slow-roll parameters.
\nThe particle physics content allows for dark matter models based on sterile neutrinos with Majorana mass terms.