Spectral action and big desert

The values of the Higgs mass are obtained for two possibilities of extending the standard model in a way compatible with the existence of a noncommutative structure at high energies. We assume the existence of a big desert between the low energy electroweak scale and the high energy scale Λ=1.1×10¹⁷ GeV, where noncommutative features become relevant. We conclude that it is extremely difficult to depart from the Higgs mass value obtained from noncommutative geometry for the standard model with three generations only.     

Synthesis and Photochromic Properties of Configurationally Varied Azobenzene Glycosides

Spatial orientation of carbohydrates is a meaningful parameter in carbohydrate recognition processes. To vary orientation of sugars with temporal and spatial resolution, photosensitive glycoconjugates with favorable photochromic properties appear to be opportune. Here, a series of azobenzene glycosides were synthesized, employing glycoside synthesis and Mills reaction, to allow “switching” of carbohydrate orientation by reversible E/Z isomerization of the azobenzene N=N double bond. Their photochromic properties were tested and effects of azobenzene substitution as well as the effect of anomeric configuration and the orientation of the sugars 2-hydroxy group were evaluated.     

Inverse Scattering Problem for the Schrödinger Operator with External Yang–Mills Potentials in Two Dimensions at Fixed Energy

ABSTRACT

We consider the Schrödinger equation in ?², with external Yang–Mills potentials that decay exponentially as |x| → ∞. We prove that the scattering amplitude at fixed positive energy determines the potentials uniquely modulo a gauge transformation, assuming that potentials are small.     

Pseudoinstantons in Metric-Affine Field Theory

In abstract Yang–Mills theory the standard instanton construction relies on the Hodge star having real eigenvalues which makes it inapplicable in the Lorentzian case. We show that for the affine connection an instanton-type construction can be carried out in the Lorentzian setting. The Lorentzian analogue of an instanton is a spacetime whose connection is metric compatible and Riemann curvature irreducible (pseudoinstanton). We suggest a metric-affine action which is a natural generalization of the Yang–Mills action and for which pseudoinstantons are stationary points. We show that a spacetime with a Ricci flat Levi-Civita connection is a pseudoinstanton, so the vacuum Einstein equation is a special case of our theory. We also find another pseudoinstanton which is a wave of torsion in Minkowski space. Analysis of the latter solution indicates the possibility of using it as a model for the neutrino.     

Hestenes' Tetrad and Spin Connections

Defining a spin connection is necessary for formulating Dirac's bispinor equation in a curved space-time. Hestenes has shown that a bispinor field is equivalent to an orthonormal tetrad of vector fields together with a complex scalar field. In this paper, we show that using Hestenes' tetrad for the spin connection in a Riemannian space-time leads to a Yang-Mills formulation of the Dirac Lagrangian in which the bispinor field Ψ is mapped to a set of SL(2,R)× U(1) gauge potentials F_α^K and a complex scalar field ρ. This result was previously proved for a Minkowski space-time using Fierz identities. As an application we derive several different non-Riemannian spin connections found in the literature directly from an arbitrary linear connection acting on the tensor fields (F_α^K, ρ). We also derive spin connections for which Dirac's bispinor equation is form invariant. Previous work has not considered form invariance of the Dirac equation as a criterion for defining a general spin connection.     

Infrared Variables for the SU(3) Yang–Mills Field

We generalize the self-dual parameterization of the SU(2) Yang–Mills field proposed by Niemi and Faddeev for describing the infrared limit of the theory to the case of the gauge group SU(3). We demonstrate that the duality property intrinsic to the SU(2) gauge field cannot be transferred automatically to the higher-rank group case. We interpret the algebraic structures appearing in the Lagrangian for the new compact variables in terms of the group products SU(2)³.     

Anti-self-dual Yang–Mills equations on noncommutative space–time

By replacing the ordinary product with the so-called -product, one can construct an analog of the anti-self-dual Yang–Mills (ASDYM) equations on the noncommutative . Many properties of the ordinary ASDYM equations turn out to be inherited by the -product ASDYM equation. In particular, the twistorial interpretation of the ordinary ASDYM equations can be extended to the noncommutative , from which one can also derive the fundamental structures for integrability such as a zero-curvature representation, an associated linear system, the Riemann–Hilbert problem, etc. These properties are further preserved under dimensional reduction to the principal chiral field model and Hitchin’s Higgs pair equations. However, some structures relying on finite dimensional linear algebra break down in the -product analogs.     

Boundary value problems for Yang—Mills fields

This paper investigates boundary value problems for Hermitian Yang—Mills equations over complex manifolds. The main result is the unique solubility of the Dirichlet problem for the Hermitian Yang—Mills equation. Connections with a number of topics are found, including the link with loop groups.     

Topological structure of the inter-band phase difference soliton in two-band superconductivity

Two-component superconductivity based on the two-band superconductor has a functional topology such as an inter-band phase difference soliton (i-soliton) to realize topological electronics (topolonics). Many gauge field theories are applied to investigate the topology of two-band superconductivity. To ease experimental and electronics applications, these theories should be refined. Weinberg–Salam theory and SU(2) (two-dimensional special unitary symmetry) gauge field theory are proper starting points. An effective extra force field because of the crystal structure and inter-band Josephson interaction, rather than spontaneous symmetry breaking, simplifies the conventional gauge field theory.