Related papers: The Mathematical Structure of $U$-Spin Amplitude S…
Splints of root system of simple lie algebras appears naturally on studies of embedding of reductive subalgebras. A splint can be used to construct a branching rules as implementation of this idea simplifies calculation of branching…
The Algebra of Physical Space (APS) is used to explore the Constructive Standard Model (CSM) of particle physics. Namely, this paper connects the spinor formalism of the APS to massive amplitudes in the CSM. A novel equivalency between…
A scheme to calculate the electronic structure of systems having a spiral magnetic structure is presented. The approach is based on the KKR (Korringa-Kohn-Rostoker) Green's function formalism which allows in combination with CPA (Coherent…
Based on the results of part I, we obtain the general form of the addition theorem for spin spherical harmonics and give explicit results in the cases involving one spin-$s'$ and one spin-$s$ spherical harmonics with $s',s=1/2$, 1, 3/2, and…
This is the first in a series of papers presenting a new understanding of scattering amplitudes based on fundamentally combinatorial ideas in the kinematic space of the scattering data. We study the simplest theory of colored scalar…
We compare among themselves two different methods for the derivation of results following from the requirement of polynomial boundedness of tree-level chiral amplitudes. It is shown that the results of the algebraic approach are valid also…
We study the path from the string scale physics to the low-energy physics in the $SU(6) \times SU(2)_R$ string-inspired model with the flavor symmetry ${\bf Z}_M \times {\bf Z}_N \times \tilde{D}_4$. The flavor symmetry controls the mass…
New results for the double spin asymmetry $A_1^{\rm p}$ and the proton longitudinal spin structure function $g_1^{\rm p}$ are presented. They were obtained by the COMPASS collaboration using polarised 200 GeV muons scattered off a…
The aim of this article is to define some new families of the special numbers. These numbers provide some further motivation for computation of combinatorial sums involving binomial coefficients and the Euler kind numbers of negative order.…
The coexistence of superconducting and charge-density-wave order in the half-filled attractive Hubbard model is interpreted as a consequence of the pseudospin SU(2) symmetry spontaneously broken to a `hidden' subgroup U(1). By topological…
We study the open version of the su$(m|n)$ supersymmetric Haldane-Shastry spin chain associated to the $BC_N$ extended root system. We first evaluate the model's partition function by modding out the dynamical degrees of freedom of the…
Massive spectral sum rules are derived for Dirac operators of $SU(N_c)$ gauge theories with $N_f$ flavors. The universal microscopic massive spectral densities of random matrix theory, where known, are all consistent with these sum rules.
We provide a combinatorial model for spin surfaces. Given a triangulation of an oriented surface, a spin structure is encoded by assigning to each triangle a preferred edge, and to each edge an orientation and a sign, subject to certain…
The skew-harmonic numbers are the partial sums of the alternating harmonic series, i.e. the expansion of log(2). We evaluate in closed form various power series and numerical series with skew-harmonic numbers. This provides a simultaneous…
We derive and prove an explicit formula for the sum of the fractional parts of certain geometric series. Although the proof is straightforward, we have been unable to locate any reference to this result. This summation formula allows us to…
We consider dynamical systems on a finite measure space fulfilling a spectral gap property and Birkhoff sums of a non-negative, non-integrable observable. For such systems we generalize strong laws of large numbers for intermediately…
Recent developments in the uses of QCD spectral sum rules (QSSR) for heavy flavours are summarized and updated. QSSR results are compared with the existing data and with the ones from alternative approaches.
The angular bispectrum of spherical random fields has recently gained an enormous importance, especially in connection with statistical inference on cosmological data. In this paper, we provide expressions for its moments of arbitrary order…
There are many conceivable possibilities of embedding the MSSM in string theory. These proceedings describe an approach which is based on grand unification in higher dimensions. This allows one to obtain global string-derived models with…
Making use of generalized calibrated geometry and G-structures we put the problem of finding string-duals with smeared backreacting flavor branes in a more mathematical setting. This more formal treatment of the problem allows us to easily…