786 research outputs found
Feynman-Jackson integrals
We introduce perturbative Feynman integrals in the context of q-calculus
generalizing the Gaussian q-integrals introduced by Diaz and Teruel. We provide
analytic as well as combinatorial interpretations for the Feynman-Jackson
integrals.Comment: Final versio
-graded Heisenberg algebras and deformed supersymmetries
The notion of -grading on the enveloping algebra generated by products of
q-deformed Heisenberg algebras is introduced for complex number in the unit
disc. Within this formulation, we consider the extension of the notion of
supersymmetry in the enveloping algebra. We recover the ordinary
grading or Grassmann parity for associative superalgebra, and a modified
version of the usual supersymmetry. As a specific problem, we focus on the
interesting limit for which the Arik and Coon deformation of the
Heisenberg algebra allows to map fermionic modes to bosonic ones in a modified
sense. Different algebraic consequences are discussed.Comment: 2 figure
First Record Of Pogoniopsis Rchb. (orchidaceae: Triphorinae) In Santa Catarina State,southern Brazil
Pogoniopsis is an endemic and myco-heterotrophic orchid genus with only two species in Brazil that can be found growing under dense canopy. Pogoniopsis schenckii is more widely distributed,with records in the states of Bahia,Minas Gerais,Paraná,Pernambuco,Rio de Janeiro,and São Paulo. Here we record P. schenckii for the first time in Santa Catarina state,southern Brazil,in a subtropical broadleaved forest,as well the genus Pogoniopsis itself,expanding its southern distribution limit. In addition,a description and a distribution map of the collected specimens are presented. © 2016 Check List and Authors.12
New connection formulae for some q-orthogonal polynomials in q-Askey scheme
New nonlinear connection formulae of the q-orthogonal polynomials, such
continuous q-Laguerre, continuous big q-Hermite, q-Meixner-Pollaczek and
q-Gegenbauer polynomials, in terms of their respective classical analogues are
obtained using a special realization of the q-exponential function as infinite
multiplicative series of ordinary exponential function
q-deformed harmonic and Clifford analysis and the q-Hermite and Laguerre polynomials
We define a q-deformation of the Dirac operator, inspired by the one
dimensional q-derivative. This implies a q-deformation of the partial
derivatives. By taking the square of this Dirac operator we find a
q-deformation of the Laplace operator. This allows to construct q-deformed
Schroedinger equations in higher dimensions. The equivalence of these
Schroedinger equations with those defined on q-Euclidean space in quantum
variables is shown. We also define the m-dimensional q-Clifford-Hermite
polynomials and show their connection with the q-Laguerre polynomials. These
polynomials are orthogonal with respect to an m-dimensional q-integration,
which is related to integration on q-Euclidean space. The q-Laguerre
polynomials are the eigenvectors of an su_q(1|1)-representation
(p,q)-Deformations and (p,q)-Vector Coherent States of the Jaynes-Cummings Model in the Rotating Wave Approximation
Classes of (p,q)-deformations of the Jaynes-Cummings model in the rotating
wave approximation are considered. Diagonalization of the Hamiltonian is
performed exactly, leading to useful spectral decompositions of a series of
relevant operators. The latter include ladder operators acting between adjacent
energy eigenstates within two separate infinite discrete towers, except for a
singleton state. These ladder operators allow for the construction of
(p,q)-deformed vector coherent states. Using (p,q)-arithmetics, explicit and
exact solutions to the associated moment problem are displayed, providing new
classes of coherent states for such models. Finally, in the limit of decoupled
spin sectors, our analysis translates into (p,q)-deformations of the
supersymmetric harmonic oscillator, such that the two supersymmetric sectors
get intertwined through the action of the ladder operators as well as in the
associated coherent states.Comment: 1+25 pages, no figure
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