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We contend that what are called Linear Canonical Transforms (LCTs) should be seen as a part of the theory of unitary irreducible representations of the '2+1' Lorentz group. The integral kernel represe...
The point-splitting computation of the gauge invariant Hamiltonian for the Schwinger model on the circle in a positive energy representation is presented.
A fractional Hamiltonian formalism is introduced for the recent combined fractional calculus of variations. The Hamilton-Jacobi partial differential equation is generalized to be applicable for system...
We use the well-known isomorphism between operator algebras and function spaces equipped with a star product to study the asymptotic properties of certain matrix sequences in which the matrix dimensio...
We consider the open spin-s XXZ quantum spin chain with nondiagonal boundary terms. By exploiting certain functional relations at roots of unity, we derive a generalized form of T-Q relation involving...
We obtain time dependent $q$-Gaussian wave-packet solutions to a non linear Schr\"odinger equation recently advanced by Nobre, Rego-Montero and Tsallis (NRT) [Phys. Rev. Lett. 106 (2011) 10601]. The N...
An outline is sketched, of applications of the ideas and the mathematical methods presented at the 19th symposium of the Hellenic Nuclear Physics Society (HNPS) in Thessaloniki, May 2010.
The integrable quantum models associated to the transfer matrices of spin 1/2 highest weight representations for the 6-vertex reflection algebra are studied in the framework of Sklyanin's quantum sepa...
A class of non-selfadjoint, $\PT$-symmetric operators is identified similar to a self-adjoint one, thus entailing the reality of the spectrum. The similarity transformation is explicitly constructed t...
Gravity, strings, modular and quasimodular forms     Gravity  strings  modular and quasimodular forms  Mathematical Physics       font style='font-size:12px;'> 2012/6/19
Modular and quasimodular forms have played an important role in gravity and string theory. Eisenstein series have appeared systematically in the determination of spectrums and partition functions, in ...
This paper deals with Cram\'er-Rao inequalities in the context of nonextensive statistics and in estimation theory. It gives characterizations of generalized q-Gaussian distributions, and introduces g...
This is the second of a series of papers in which we develop a "discretization approach" for the rigorous realization of the non-Abelian Chern-Simons path integral for manifolds M of the form M=Sigma ...
We introduce a family of exactly-solvable two-dimensional Hamiltonians whose wave functions are given in terms of Laguerre and exceptional Jacobi polynomials. The Hamiltonians contain purely quantum t...
We find further implications of the BMV conjecture, which states that for hermitian matrices A and B, the function Tr exp(A - t B) is the Laplace transform of a positive measure.
Augmented down-up algebras and uniform posets     Uniform poset  dual polar space  dual polar graph  down-up algebra       font style='font-size:12px;'> 2012/6/19
Motivated by the structure of the uniform posets we introduce the notion of an augmented down-up (or ADU) algebra. We discuss how ADU algebras are related to the down-up algebras defined by Benkart an...

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