Related papers: $R$-matrices for Elliptic Calogero-Moser Models
We present a three-loop model of neutrino mass whose most-general Lagrangian possesses a softly-broken accidental $Z_2$ symmetry. In the limit that a single parameter vanishes, $\lambda\rightarrow0$, the $Z_2$ symmetry becomes exact and the…
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Matroid theory provides a unifying framework for studying dependence across combinatorics, geometry, and applications ranging from rigidity to statistics. In this work, we study circuit varieties of matroids, defined by their minimal…
We analyze the complex analytic properties of Classical (tree-level) S-matrices for four scalar particles with s-t crossing symmetry, involving an infinite number of exchanges. Under suitable analytic conditions, we demonstrate that such…
We carry out a fully analytical study of the phenomenology of $\alpha$-attractor T-models defined by the potential $V = V_0\tanh^ p\left(\lambda \phi/M_{pl}\right)$. We obtain expressions for the number of e-folds during inflation $N_{ke}$…
Using noncommutative geometry, the standard tools of differential geometry can be extended to a broad class of spaces whose coordinates are noncommuting operators acting on a Hilbert space. In the simplest case of coordinates being matrix…
Relations between the free motion on the GL^+(n, R) group manifold and the dynamics of an n-particle system with spin degrees of freedom on a line interacting with the pairwise 1/sinh^2 x ``potential'' (Euler-Calogero-Sutherland model) is…
The matrix elements of relativistic nucleon-nucleon $(NN)$ potentials are calculated directly from the nonrelativistic potentials as a function of relative $NN$ momentum vectors, without using a partial wave decomposition. To this aim, the…
In this paper, we construct a quadratic r-matrix structure for the classical rational BC(n) Ruijsenaars-Schneider-van Diejen system with the maximal number of three independent coupling parameters. As a byproduct, we provide a Lax…
The traditional class of elliptical distributions is extended to allow for asymmetries. A completely robust dispersion matrix estimator (the `spectral estimator') for the new class of `generalized elliptical distributions' is presented. It…
We construct a separation of variables for the classical n-particle Ruijsenaars system (the relativistic analog of the elliptic Calogero-Moser system). The separated coordinates appear as the poles of the properly normalised eigenvector…
Recently, we have proposed a quark mass matrix model based on U(3)$\times$U(3)$'$ family symmetry, in which up- and down-quark mass matrices $M_u$ and $M_d$ are described only by complex parameters $a_u $ and $a_d $, respectively. When we…
This paper studies sparse elliptic random matrix models which generalize both the classical elliptic ensembles and sparse i.i.d. matrix models by incorporating correlated entries and a tunable sparsity parameter $p_n$. Each $n\times n$…
In this work we generalise previous results connecting (rational) Gaudin magnet models and classical separation of variables. It is shown that the connection persists for the case of linear r-matrix algebra which corresponds to the…
We discuss the electromagnetic properties of both a charged free particle, and a charged particle bounded by an harmonic potential, within collapse models. By choosing a particularly simple, yet physically relevant, collapse model, and…
We consider quantum motion on S3 perturbed by the trigonometric Scarf potential (Scarf I) with one internal quantized dimensionless parameter, l, the ordinary orbital angular momentum value, and another, continuous parameter, b, through…
We develop a new, systematic approach towards studying the integrability of the ordinary Calogero-Moser-Sutherland models as well as the elliptic Calogero models associated with arbitrary (semi-)simple Lie algebras and with symmetric pairs…
We derive the lepton number violating dimension-five and dimension-seven operators, relevant for neutrino mass generation, in the Minimal Supersymmetry Standard Model without R-parity (the $/R$MSSM) by using the effective Lagrangian method.…
By applying the renormalization group equation, it has been shown that the effective potential $V$ in the massless $\phi_4^4$ model and in massless scalar quantum electrodynamics is independent of the scalar field. This analysis is extended…