864 research outputs found
On the ternary complex analysis and its applications
Previouly a possible extension of the complex number, together with its
connected trigonometry was introduced. In this paper we focuss on the simplest
case of ternary complex numbers. Then, some types of holomorphicity adapted to
the ternary complex numbers and the corresponding results upon integration of
differential forms are given. Several physical applications are given, and in
particuler one type of holomorphic function gives rise to a new form of
stationary magnetic field. The movement of a monopole type object in this field
is then studied and shown to be integrable. The monopole scattering in the
ternary field is finally studied.Comment: LaTeX 28 page
On hypergeometric series reductions from integral representations, the Kampe de Feriet function, and elsewhere
Single variable hypergeometric functions pFq arise in connection with the
power series solution of the Schrodinger equation or in the summation of
perturbation expansions in quantum mechanics. For these applications, it is of
interest to obtain analytic expressions, and we present the reduction of a
number of cases of pFp and p+1F_p, mainly for p=2 and p=3. These and related
series have additional applications in quantum and statistical physics and
chemistry.Comment: 17 pages, no figure
Controlling Effect of Geometrically Defined Local Structural Changes on Chaotic Hamiltonian Systems
An effective characterization of chaotic conservative Hamiltonian systems in
terms of the curvature associated with a Riemannian metric tensor derived from
the structure of the Hamiltonian has been extended to a wide class of potential
models of standard form through definition of a conformal metric. The geodesic
equations reproduce the Hamilton equations of the original potential model
through an inverse map in the tangent space. The second covariant derivative of
the geodesic deviation in this space generates a dynamical curvature, resulting
in (energy dependent) criteria for unstable behavior different from the usual
Lyapunov criteria. We show here that this criterion can be constructively used
to modify locally the potential of a chaotic Hamiltonian model in such a way
that stable motion is achieved. Since our criterion for instability is local in
coordinate space, these results provide a new and minimal method for achieving
control of a chaotic system
Integral representations of q-analogues of the Hurwitz zeta function
Two integral representations of q-analogues of the Hurwitz zeta function are
established. Each integral representation allows us to obtain an analytic
continuation including also a full description of poles and special values at
non-positive integers of the q-analogue of the Hurwitz zeta function, and to
study the classical limit of this q-analogue. All the discussion developed here
is entirely different from the previous work in [4]Comment: 14 page
A massive Feynman integral and some reduction relations for Appell functions
New explicit expressions are derived for the one-loop two-point Feynman
integral with arbitrary external momentum and masses and in D
dimensions. The results are given in terms of Appell functions, manifestly
symmetric with respect to the masses . Equating our expressions with
previously known results in terms of Gauss hypergeometric functions yields
reduction relations for the involved Appell functions that are apparently new
mathematical results.Comment: 19 pages. To appear in Journal of Mathematical Physic
On structure constants and fusion rules in the SL(2,\BC)/SU(2) WZNW model
A closed formula for the structure constants in the SL(2,C)/SU(2) WZNW model
is derived by a method previously used in Liouville theory. With the help of a
reflection amplitude that follows from the structure constants one obtains a
proposal for the fusion rules from canonical quantization. Taken together these
pieces of information allow an unambigous definition of any genus zero n-point
function.Comment: 25 pages, AMSLATEX2e, discussion of canonical quantization and fusion
rules clarified, a few correction
Nuclear Effects on Heavy Boson Production at RHIC and LHC
We predict W and Z transverse momentum distributions from proton-proton and
nuclear collisions at RHIC and LHC. A resummation formalism with power
corrections to the renormalization group equations is used. The dependence of
the resummed QCD results on the non-perturbative input is very weak for the
systems considered. Shadowing effects are discussed and found to be unimportant
at RHIC, but important for LHC. We study the enhancement of power corrections
due to multiple scattering in nuclear collisions and numerically illustrate the
weak effects of the dependence on the nuclear mass.Comment: 21 pages, 11 figure
On the Equivalence Between Type I Liouville Dynamical Systems in the Plane and the Sphere
ProducciĂłn CientĂficaSeparable Hamiltonian systems either in sphero-conical coordinates on an S2 sphere or in elliptic coordinates on a R2 plane are described in a unified way. A back and forth route connecting these Liouville Type I separable systems is unveiled. It is shown how the gnomonic projection and its inverse map allow us to pass from a Liouville Type I separable system with a spherical configuration space
to its Liouville Type I partners where the configuration space is a plane and back. Several selected spherical separable systems and their planar cousins are discussed in a classical context
On two-dimensional Bessel functions
The general properties of two-dimensional generalized Bessel functions are
discussed. Various asymptotic approximations are derived and applied to analyze
the basic structure of the two-dimensional Bessel functions as well as their
nodal lines.Comment: 25 pages, 17 figure
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