1,608 research outputs found
Noneuclidean Tessellations and their relation to Reggie Trajectories
The coefficients in the confluent hypergeometric equation specify the Regge
trajectories and the degeneracy of the angular momentum states. Bound states
are associated with real angular momenta while resonances are characterized by
complex angular momenta. With a centrifugal potential, the half-plane is
tessellated by crescents. The addition of an electrostatic potential converts
it into a hydrogen atom, and the crescents into triangles which may have
complex conjugate angles; the angle through which a rotation takes place is
accompanied by a stretching. Rather than studying the properties of the wave
functions themselves, we study their symmetry groups. A complex angle indicates
that the group contains loxodromic elements. Since the domain of such groups is
not the disc, hyperbolic plane geometry cannot be used. Rather, the theory of
the isometric circle is adapted since it treats all groups symmetrically. The
pairing of circles and their inverses is likened to pairing particles with
their antiparticles which then go one to produce nested circles, or a
proliferation of particles. A corollary to Laguerre's theorem, which states
that the euclidean angle is represented by a pure imaginary projective
invariant, represents the imaginary angle in the form of a real projective
invariant.Comment: 27 pages, 4 figure
Causal Space-Times on a Null Lattice
I investigate a discrete model of quantum gravity on a causal null-lattice
with \SLC structure group. The description is geometric and foliates in a
causal and physically transparent manner. The general observables of this model
are constructed from local Lorentz symmetry considerations only. For smooth
configurations, the local lattice actions reduce to the Hilbert-Palatini
action, a cosmological term and the three topological terms of dimension four
of Pontyagin, Euler and Nieh-Yan. Consistency conditions for a topologically
hypercubic complex with null 4-simplexes are derived and a topological lattice
theory that enforces these non-local constraints is constructed. The lattice
integration measure is derived from an \SLC-invariant integration measure by
localization of the non-local structure group. This measure is unique up to a
density that depends on the local 4-volume. It can be expressed in terms of
manifestly coordinate invariant geometrical quantities. The density provides an
invariant regularization of the lattice integration measure that suppresses
configurations with small local 4-volumes. Amplitudes conditioned on geodesic
distances between local observables have a physical interpretation and may have
a smooth ultraviolet limit. Numerical studies on small lattices in the
unphysical strong coupling regime of large imaginary cosmological constant
suggest that this model of triangulated causal manifolds is finite. Two
topologically different triangulations of space-time are discussed: a single,
causally connected universe and a duoverse with two causally disjoint connected
components. In the duoverse, two hypercubic sublattices are causally disjoint
but the local curvature depends on fields of both sublattices. This may
simulate effects of dark matter in the continuum limit.Comment: Greatly improved version, new numerics, appendices, etc.. 42 pages,
14 figure
Mission Analysis Program for Solar Electric Propulsion (MAPSEP). Volume 3: Program manual
The internal structure of MAPSEP is described. Topics discussed include: macrologic, variable definition, subroutines, and logical flow. Information is given to facilitate modifications to the models and algorithms of MAPSEP
Rocket exhaust plume computer program improvement. Volume 1: Summary: Method of characteristics nozzle and plume programs
A summary is presented of the various documents that discuss and describe the computer programs and analysis techniques which are available for rocket nozzle and exhaust plume calculations. The basic method of characteristics program is discussed, along with such auxiliary programs as the plume impingement program, the plot program and the thermochemical properties program
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