34,327 research outputs found
Induced Gravity II: Grand Unification
As an illustration of a renormalizable, asymptotically-free model of induced
gravity, we consider an gauge theory interacting with a real scalar
multiplet in the adjoint representation. We show that dimensional transmutation
can occur, spontaneously breaking to while
inducing the Planck mass and a positive cosmological constant, all proportional
to the same scale . All mass ratios are functions of the values of coupling
constants at that scale. Below this scale (at which the Big Bang may occur),
the model takes the usual form of Einstein-Hilbert gravity in de Sitter space
plus calculable corrections. We show that there exist regions of parameter
space in which the breaking results in a local minimum of the effective action,
and a {\bf positive} dilaton from two-loop corrections
associated with the conformal anomaly. Furthermore, unlike the singlet case we
considered previously, some minima lie within the basin of attraction of the
ultraviolet fixed point. Moreover, the asymptotic behavior of the coupling
constants also lie within the range of convergence of the Euclidean path
integral, so there is hope that there will be candidates for sensible vacua.
Although open questions remain concerning unitarity of all such renormalizable
models of gravity, it is not obvious that, in curved backgrounds such as those
considered here, unitarity is violated. In any case, any violation that may
remain will be suppressed by inverse powers of the reduced Planck mass.Comment: 44 pages, 5 figures, 2 tables. v2 has new discussion concerning
stability of SSB plus related appendix. Additional references added. v3 is
version to be published; contains minor revision
Zero modes in de Sitter background
There are five well-known zero modes among the fluctuations of the metric of
de~Sitter (dS) spacetime. For Euclidean signature, they can be associated with
certain spherical harmonics on the sphere, viz., the vector
representation of the global isometry. They appear, for example,
in the perturbative calculation of the on-shell effective action of dS space,
as well as in models containing matter fields. These modes are shown to be
associated with collective modes of corresponding to certain coherent
fluctuations. When dS space is embedded in flat five dimensions they may
be seen as a legacy of translation of the center of the sphere. Rigid
translations of the -sphere on leave the classical action invariant
but are unobservable displacements from the point of view of gravitational
dynamics on Thus, unlike similar moduli, the center of the sphere is not
promoted to a dynamical degree of freedom. As a result, these zero modes do not
signify the possibility of physically realizable fluctuations or flat
directions for the metric of dS space. They are not associated with Killing
vectors on but can be with certain non-isometric, conformal Killing forms
that locally correspond to a rescaling of the volume element
For convenience, we frame our discussion in the context of renormalizable
gravity, but the conclusions apply equally to the corresponding zero modes in
Einstein gravity. We expect that these zero modes will be present to all orders
in perturbation theory. They will occur for Lorentzian signature as well, so
long as the hyperboloid is locally stable, but there remain certain
infrared issues that need to be clarified. We conjecture that they will appear
in any gravitational theory having dS background as a locally stable solution
of the effective action, regardless of whether additional matter is included.Comment: v4, 28pages, no figures; final journal form, minor changes in text
and refs from v
A study of wide bandwidth directional patterns from circular arrays
Passive radar warning receivers use amplitude comparison direction-finding to determine the angle of arrival of incoming signals. This type of direction-finding system requires wideband azimuth beams that do not change in shape with frequency. The subject of this thesis is the synthesis of wideband beams using a circular array. In the first part of this thesis the excitation of the circular array is analysed using the concept of 'phase modes': the orthogonal terms of a spatial Fourier series. If the variations in phase and amplitude of these modes with frequency are corrected, azimuth patterns formed from these modes are instantaneously wideband. Pattern synthesis uses the principle of linear array equivalence, allowing us to apply low sidelobe techniques developed for linear arrays to the phase modes. The design of the experimental system, operating over the frequency range 8 to 12 GHz, is subsequently presented. The characteristics of the phase modes excited on a four element monopoles array were evaluated, showing that the array could be used to form a low sidelobe beams. The initial beamformer design used a Butler matrix constructed from microwave directional couplers to excite the phase modes. By utilising microstrip compensation networks, the variation in phase and amplitude of these modes with frequency is corrected. Multiple beams are formed from the compensated modes by a second matrix. Both theoretical and measured results showed that the phase and amplitude errors introduced by this complicated network were unacceptable. Multiple beams were not demonstrated in this study. A simplified matrix design was developed to demonstrate a low sidelobe (-28 dB) beam at a single fi*equency. A weighted corporate feed was developed to demonstrate instantaneously wideband pattern synthesis of a single beam. The element excitation required to form a low sidelobe pattern was calculated using phase mode theory. The frequency-dependent element excitation was practically realised using the microstrip networks. Anechoic chamber measurements of the synthesised wideband beam showed that the variation in the -3 dB beamwidth across the band 8 to 12 GHz was less than ±3°. The sidelobe level was below -20 dB. Theoretical calculations limit the frequency bandwidth for this synthesis technique to about one octave. A wideband sin(Nx)/Nsin(x) pattern was also produced to demonstrate the versatility of this synthesis technique
Mixed mode oscillations in a conceptual climate model
Much work has been done on relaxation oscillations and other simple
oscillators in conceptual climate models. However, the oscillatory patterns in
climate data are often more complicated than what can be described by such
mechanisms. This paper examines complex oscillatory behavior in climate data
through the lens of mixed-mode oscillations. As a case study, a conceptual
climate model with governing equations for global mean temperature, atmospheric
carbon, and oceanic carbon is analyzed. The nondimensionalized model is a
fast/slow system with one fast variable (corresponding to ice volume) and two
slow variables (corresponding to the two carbon stores). Geometric singular
perturbation theory is used to demonstrate the existence of a folded node
singularity. A parameter regime is found in which (singular) trajectories that
pass through the folded node are returned to the singular funnel in the
limiting case where . In this parameter regime, the model has a
stable periodic orbit of type for some . To our knowledge, it is the
first conceptual climate model demonstrated to have the capability to produce
an MMO pattern.Comment: 28 pages, 11 figure
The non-linear transient behavior of second, third and fourth order phase-locked loops
Non-linear transient behavior of second, third, and fourth order phase-locked loop
Representation-theoretic derivation of the Temperley-Lieb-Martin algebras
Explicit expressions for the Temperley-Lieb-Martin algebras, i.e., the
quotients of the Hecke algebra that admit only representations corresponding to
Young diagrams with a given maximum number of columns (or rows), are obtained,
making explicit use of the Hecke algebra representation theory. Similar
techniques are used to construct the algebras whose representations do not
contain rectangular subdiagrams of a given size.Comment: 12 pages, LaTeX, to appear in J. Phys.
Algebras in Higher Dimensional Statistical Mechanics - the Exceptional Partition (MEAN Field) Algebras
We determine the structure of the partition algebra (a generalized
Temperley-Lieb algebra) for specific values of Q \in \C, focusing on the
quotient which gives rise to the partition function of site -state Potts
models (in the continuous formulation) in arbitrarily high lattice
dimensions (the mean field case). The algebra is non-semi-simple iff is a
non-negative integer less than . We determine the dimension of the key
irreducible representation in every specialization.Comment: 4 page
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