635 research outputs found
Continuously Crossing u=z in the H3+ Boundary CFT
For AdS boundary conditions, we give a solution of the H3+ two point function
involving degenerate field with SL(2)-label b^{-2}/2, which is defined on the
full (u,z) unit square. It consists of two patches, one for z<u and one for
u<z. Along the u=z "singularity", the solutions from both patches are shown to
have finite limits and are merged continuously as suggested by the work of
Hosomichi and Ribault. From this two point function, we can derive
b^{-2}/2-shift equations for AdS_2 D-branes. We show that discrete as well as
continuous AdS_2 branes are consistent with our novel shift equations without
any new restrictions.Comment: version to appear in JHEP - 12 pages now; sign error with impact on
some parts of the interpretation fixed; material added to become more
self-contained; role of bulk-boundary OPE in section 4 more carefully
discussed; 3 references adde
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
A Generalization of Chetaev's Principle for a Class of Higher Order Non-holonomic Constraints
The constraint distribution in non-holonomic mechanics has a double role. On
one hand, it is a kinematic constraint, that is, it is a restriction on the
motion itself. On the other hand, it is also a restriction on the allowed
variations when using D'Alembert's Principle to derive the equations of motion.
We will show that many systems of physical interest where D'Alembert's
Principle does not apply can be conveniently modeled within the general idea of
the Principle of Virtual Work by the introduction of both kinematic constraints
and variational constraints as being independent entities. This includes, for
example, elastic rolling bodies and pneumatic tires. Also, D'Alembert's
Principle and Chetaev's Principle fall into this scheme. We emphasize the
geometric point of view, avoiding the use of local coordinates, which is the
appropriate setting for dealing with questions of global nature, like
reduction.Comment: 27 pages. Journal of Mathematical Physics (to zappear
Multi-Dimensional Hermite Polynomials in Quantum Optics
We study a class of optical circuits with vacuum input states consisting of
Gaussian sources without coherent displacements such as down-converters and
squeezers, together with detectors and passive interferometry (beam-splitters,
polarisation rotations, phase-shifters etc.). We show that the outgoing state
leaving the optical circuit can be expressed in terms of so-called
multi-dimensional Hermite polynomials and give their recursion and
orthogonality relations. We show how quantum teleportation of photon
polarisation can be modelled using this description.Comment: 10 pages, submitted to J. Phys. A, removed spurious fil
Geodesics around Weyl-Bach's Ring Solution
We explore some of the gravitational features of a uniform ring both in the
Newtonian potential theory and in General Relativity. We use a spacetime
associated to a Weyl static solution of the vacuum Einstein's equations with
ring like singularity. The Newtonian motion for a test particle in the
gravitational field of the ring is studied and compared with the corresponding
geodesic motion in the given spacetime. We have found a relativistic peculiar
attraction: free falling particle geodesics are lead to the inner rim but never
hit the ring.Comment: 8 figures, 14 pages. LaTeX w/ subfigure, graphic
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
The restricted two-body problem in constant curvature spaces
We perform the bifurcation analysis of the Kepler problem on and .
An analogue of the Delaunay variables is introduced. We investigate the motion
of a point mass in the field of the Newtonian center moving along a geodesic on
and (the restricted two-body problem). When the curvature is small,
the pericenter shift is computed using the perturbation theory. We also present
the results of the numerical analysis based on the analogy with the motion of
rigid body.Comment: 29 pages, 7 figure
Projective dynamics and classical gravitation
Given a real vector space V of finite dimension, together with a particular
homogeneous field of bivectors that we call a "field of projective forces", we
define a law of dynamics such that the position of the particle is a "ray" i.e.
a half-line drawn from the origin of V. The impulsion is a bivector whose
support is a 2-plane containing the ray. Throwing the particle with a given
initial impulsion defines a projective trajectory. It is a curve in the space
of rays S(V), together with an impulsion attached to each ray. In the simplest
example where the force is identically zero, the curve is a straight line and
the impulsion a constant bivector. A striking feature of projective dynamics
appears: the trajectories are not parameterized.
Among the projective force fields corresponding to a central force, the one
defining the Kepler problem is simpler than those corresponding to other
homogeneities. Here the thrown ray describes a quadratic cone whose section by
a hyperplane corresponds to a Keplerian conic. An original point of view on the
hidden symmetries of the Kepler problem emerges, and clarifies some remarks due
to Halphen and Appell. We also get the unexpected conclusion that there exists
a notion of divergence-free field of projective forces if and only if dim V=4.
No metric is involved in the axioms of projective dynamics.Comment: 20 pages, 4 figure
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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