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Canonical description of the D=10 superstring action involving supertwistor variables generalizing Penrose-Ferber supertwistors is developed. Primary and secondary constraints are identified and arranged into the first- and second-class…
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(Quasi-)Poisson-Lie T-duality of string effective actions is described in the framework of generalized geometry of Courant algebroids. The approach is based on a generalization of Riemannian geometry in the context of Courant algebroids,…
Directional Poisson wavelets, being directional derivatives of Poisson kernel, are introduced on $n$-dimensional spheres. It is shown that, slightly modified and together with another wavelet family, they are an admissible wavelet pair…
The elastic backward proton-deuteron scattering is analyzed within a fully covariant approach based on the invariant expansion of the reaction amplitude. The method of calculation of any observables for any reaction mechanism is developed.…
The Dunkl operators associated to a dihedral group are a pair of differential-difference operators that generate a commutative algebra acting on differentiable functions in $\mathbb{R}^2$. The intertwining operator intertwines between this…
This is the first in a series of papers on Poisson formalism for the cubic nonlinear Schr\"{o}dinger equation with repulsive nonlinearity and its relation to complex geometry. In this paper we study general continuous potentials. We…
As shown in earlier work, skew-adjoint linear differential operators, mapping efforts into flows, give rise to Dirac structures on a bounded spatial domain by a proper definition of boundary variables. In the present paper this is extended…
The analysis of the radial distribution function of a system provides a possible procedure for uncovering interaction rules between individuals out of collective movement patterns. This approach from classical statistical mechanics has…
We construct categorical braid group actions from 2-representations of a Heisenberg algebra. These actions are induced by certain complexes which generalize spherical (Seidel-Thomas) twists and are reminiscent of the Rickard complexes…
We study a deformation of a $2$-graded Poisson algebra where the functions of the phase space variables are complemented by linear functions of parity odd velocities. The deformation is carried by a $2$-form $B$-field and a bivector $\Pi$,…
In classical and quantum mechanical systems on manifolds with gauge-field fluxes, constants of motion are constructed from gauge-covariant extensions of Killing vectors and tensors. This construction can be carried out using a manifestly…
Let X be a smooth algebraic variety over a field K containing the real numbers. We introduce the notion of twisted associative (resp. Poisson) deformation of the structure sheaf of X. These are stack-like versions of usual deformations. We…
A KdV flow is constructed on a space whose structure is described in terms of the spectrum of the underlying Schr\"odinger operators. The space includes the conventional decaying functions and ergodic ones. Especially any smooth almost…
Emphasizing the role of Gerstenhaber algebras and of higher derived brackets in the theory of Lie algebroids, we show that the several Lie algebroid brackets which have been introduced in the recent literature can all be defined in terms of…
We give a definition of scattering matrices based on the asymptotic behaviors of generalized eigenfunctions and show that these scattering matrices are equivalent to the ones defined by wave-operator approach in long-range $N$-body…
A time-dependent completely integrable Hamiltonian system is proved to admit the action-angle coordinates around any regular instantly compact invariant manifold. Written relative to these coordinates, its Hamiltonian and first integrals…
We develop direct and inverse scattering theory for Jacobi operators with steplike quasi-periodic finite-gap background in the same isospectral class. We derive the corresponding Gel'fand-Levitan-Marchenko equation and find minimal…
A valuable approach to the analysis of hadron physics observables is provided by QCD's equations-of-motion; namely, the Dyson-Schwinger equations. Drawing from a diverse collection of predictions, we revisit: $\gamma \gamma^* \to$ neutral…