Related papers: Comments on Supersymmetric Vector and Matrix Model…
We give a simplified account of the properties of the transfer matrix for a complex one-dimensional potential, paying special attention to the particular instance of unidirectional invisibility. In appropriate variables, invisible…
Using renormalization group techniques, we examine several interesting relations among masses and mixing angles of quarks and leptons in the Standard Model. We extend the analysis to the minimal supersymmetric extension to determine its…
Random matrix theory allows one to deduce the eigenvalue spectrum of a large matrix given only statistical information about its elements. Such results provide insight into what factors contribute to the stability of complex dynamical…
A unified theory of four-dimensional gravity together with the standard model is presented, with supersymmetry breaking of M-theory at a TeV. Masses of the the known particles are derived. The cosmological constant is quantum generated to…
It is well known that over an infinite field the ring of symmetric functions in a finite number of variables is isomorphic to the one of polynomial functions on matrices that are invariants by the action of conjugation by general linear…
Based on a reduction processing, we rewrite a hypergeometric term as the sum of the difference of a hypergeometric term and a reduced hypergeometric term (the reduced part, in short). We show that when the initial hypergeometric term has a…
We develop a systematic algorithm for constructing an N-fold supersymmetric system from a given vector space invariant under one of the supercharges. Applying this algorithm to spaces of monomials, we construct a new multi-parameter family…
We extend the recent study of the k-body embedded Gaussian ensembles by Benet et al. (Phys. Rev. Lett. 87 (2001) 101601-1 and Ann. Phys. 292 (2001) 67) and by Asaga et al. (cond-mat/0107363 and cond-mat/ 0107364). We show that central…
In this work we investigate connections between superalgebras and their realizations in terms of particles, branes and field theory models. We start from Poincar\'e superalgebras with brane charges and study its representations. The…
We show that the quantum Hamilton Jacobi approach to a class of quantum mechanical bound state problems and the Gaussian orthogonal ensemble of random matrix theory are equivalent. The Berry connection for both problems is identical to…
The review is devoted to the integrable properties of the Generalized Kontsevich Model which is supposed to be an universal matrix model to describe the conformal field theories with $c<1$. It is shown that the deformations of the…
We consider an ensemble of $2\times 2$ normal matrices with complex entries representing operators in the quantum mechanics of 2 - level parity-time reversal (PT) symmetric systems. The randomness of the ensemble is endowed by obtaining…
We construct the action of a relativistic spinning particle from a non-linear realization of a space-time odd vector extension of the Poincar\'e group. For particular values of the parameters appearing in the lagrangian the model has a…
We consider certain large random matrices, called random inner-product kernel matrices, which are essentially given by a nonlinear function $f$ applied entrywise to a sample-covariance matrix, $f(X^TX)$, where $X \in \mathbb{R}^{d \times…
We show that rigid supersymmetry theories in four dimensions can be extended to give supersymmetric trace (or generalized quantum) dynamics theories, in which the supersymmetry algebra is represented by the generalized Poisson bracket of…
We apply the random-matrix theory to the car-parking problem. For this purpose, we adopt a Coulomb gas model that associates the coordinates of the gas particles with the eigenvalues of a random matrix. The nature of interaction between the…
The Chiral Random Matrix Model or the Gaussian Penner Model (generalized Laguerre ensemble) is re-examined in the light of the results which have been found in double well matrix models [D97,BD99] and subtleties discovered in the single…
Dynamic equations that are the simplest conformally invariant generalization of Einstein equations with cosmological term are considered. Dimensions and Weyl weights of the additional geometrical fields (the vector and the antisymmetric…
The existence of neutrino mass and mixing is a strong pointer towards physics beyond the standard model. An overview of the possibility of having neutrino masses in supersymmetric theories is attempted here. Some of the recent works…
Statistical models that possess symmetry arise in diverse settings such as random fields associated to geophysical phenomena, exchangeable processes in Bayesian statistics, and cyclostationary processes in engineering. We formalize the…