359 research outputs found
Diffusion due to the Beam-Beam Interaction and Fluctuating Fields in Hadron Colliders
Random fluctuations in the tune, beam offsets and beam size in the presence
of the beam-beam interaction are shown to lead to significant particle
diffusion and emittance growth in hadron colliders. We find that far from
resonances high frequency noise causes the most diffusion while near resonances
low frequency noise is responsible for the large emittance growth observed.
Comparison of different fluctuations shows that offset fluctuations between the
beams causes the largest diffusion for particles in the beam core.Comment: 5 pages, 3 postscript figure
Witten's 2+1 gravity on R x (Klein bottle)
Witten's formulation of 2+1 gravity is investigated on the nonorientable
three-manifold R x (Klein bottle). The gauge group is taken to consist of all
four components of the 2+1 Poincare group. We analyze in detail several
components of the classical solution space, and we show that from four of the
components one can recover nondegenerate spacetime metrics. In particular, from
one component we recover metrics for which the Klein bottles are spacelike. An
action principle is formulated for bundles satisfying a certain orientation
compatibility property, and the corresponding components of the classical
solution space are promoted into a phase space. Avenues towards quantization
are briefly discussed.Comment: 33 pages, REVTeX v3.0, 3 figures in a separate PostScript fil
The Torus Universe in the Polygon Approach to 2+1-Dimensional Gravity
In this paper we describe the matter-free toroidal spacetime in 't Hooft's
polygon approach to 2+1-dimensional gravity (i.e. we consider the case without
any particles present). Contrary to earlier results in the literature we find
that it is not possible to describe the torus by just one polygon but we need
at least two polygons. We also show that the constraint algebra of the polygons
closes.Comment: 18 pages Latex, 13 eps-figure
Chern-Simons Quantization of (2+1)-Anti-De Sitter Gravity on a Torus
Chern-Simons formulation of 2+1 dimensional Einstein gravity with a negative
cosmological constant is investigated when the spacetime has the topology . The physical phase space is shown to be a direct product of two
sub-phase spaces each of which is a non-Hausdorff manifold plus a set with
nonzero codimensions. Spacetime geometrical interpretation of each point in the
phase space is also given and we explain the 1 to 2 correspondence with the ADM
formalism from the geometrical viewpoint. In quantizing this theory, we
construct a "modified phase space" which is a cotangnt bundle on a torus. We
also provide a modular invariant inner product and investigate the relation to
the quantum theory which is directly related to the spinor representation of
the ADM formalism. (This paper is the revised version of a previous
paper(hep-th/9312151). The wrong discussion on the topology of the phase space
is corrected.)Comment: latex 28 page
Loop Representations for 2+1 Gravity on a Torus
We study the loop representation of the quantum theory for 2+1 dimensional
general relativity on a manifold, , where
is the torus, and compare it with the connection representation
for this system. In particular, we look at the loop transform in the part of
the phase space where the holonomies are boosts and study its kernel. This
kernel is dense in the connection representation and the transform is not
continuous with respect to the natural topologies, even in its domain of
definition. Nonetheless, loop representations isomorphic to the connection
representation corresponding to this part of the phase space can still be
constructed if due care is taken. We present this construction but note that
certain ambiguities remain; in particular, functions of loops cannot be
uniquely associated with functions of connections.Comment: 24 journal or 52 preprint pages, revtex, SU-GP-93/3-
A Spinning Anti-de Sitter Wormhole
We construct a 2+1 dimensional spacetime of constant curvature whose spatial
topology is that of a torus with one asymptotic region attached. It is also a
black hole whose event horizon spins with respect to infinity. An observer
entering the hole necessarily ends up at a "singularity"; there are no inner
horizons.
In the construction we take the quotient of 2+1 dimensional anti-de Sitter
space by a discrete group Gamma. A key part of the analysis proceeds by
studying the action of Gamma on the boundary of the spacetime.Comment: Latex, 28 pages, 7 postscript figures included in text, a Latex file
without figures can be found at http://vanosf.physto.se/~stefan/spinning.html
Replaced with journal version, minor change
3-manifolds which are spacelike slices of flat spacetimes
We continue work initiated in a 1990 preprint of Mess giving a geometric
parameterization of the moduli space of classical solutions to Einstein's
equations in 2+1 dimensions with cosmological constant 0 or -1 (the case +1 has
been worked out in the interim by the present author). In this paper we make a
first step toward the 3+1-dimensional case by determining exactly which closed
3-manifolds M^3 arise as spacelike slices of flat spacetimes, and by finding
all possible holonomy homomorphisms pi_1(M^3) to ISO(3,1).Comment: 10 page
Black Holes and Wormholes in 2+1 Dimensions
A large variety of spacetimes---including the BTZ black holes---can be
obtained by identifying points in 2+1 dimensional anti-de Sitter space by means
of a discrete group of isometries. We consider all such spacetimes that can be
obtained under a restriction to time symmetric initial data and one asymptotic
region only. The resulting spacetimes are non-eternal black holes with
collapsing wormhole topologies. Our approach is geometrical, and we discuss in
detail: The allowed topologies, the shape of the event horizons, topological
censorship and trapped curves.Comment: 23 pages, LaTeX, 11 figure
Dimension of the Torelli group for Out(F_n)
Let T_n be the kernel of the natural map from Out(F_n) to GL(n,Z). We use
combinatorial Morse theory to prove that T_n has an Eilenberg-MacLane space
which is (2n-4)-dimensional and that H_{2n-4}(T_n,Z) is not finitely generated
(n at least 3). In particular, this recovers the result of Krstic-McCool that
T_3 is not finitely presented. We also give a new proof of the fact, due to
Magnus, that T_n is finitely generated.Comment: 27 pages, 9 figure
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