342 research outputs found
Extending Elliptic Curve Chabauty to higher genus curves
We give a generalization of the method of "Elliptic Curve Chabauty" to higher
genus curves and their Jacobians. This method can sometimes be used in
conjunction with covering techniques and a modified version of the Mordell-Weil
sieve to provide a complete solution to the problem of determining the set of
rational points of an algebraic curve .Comment: 24 page
Phase transition in the transverse Ising model using the extended coupled-cluster method
The phase transition present in the linear-chain and square-lattice cases of
the transverse Ising model is examined. The extended coupled cluster method
(ECCM) can describe both sides of the phase transition with a unified approach.
The correlation length and the excitation energy are determined. We demonstrate
the ability of the ECCM to use both the weak- and the strong-coupling starting
state in a unified approach for the study of critical behavior.Comment: 10 pages, 7 eps-figure
Trapped Particle Stability for the Kinetic Stabilizer
A kinetically stabilized axially symmetric tandem mirror (KSTM) uses the
momentum flux of low-energy, unconfined particles that sample only the outer
end-regions of the mirror plugs, where large favorable field-line curvature
exists. The window of operation is determined for achieving MHD stability with
tolerable energy drain from the kinetic stabilizer. Then MHD stable systems are
analyzed for stability of the trapped particle mode. This mode is characterized
by the detachment of the central-cell plasma from the kinetic stabilizer region
without inducing field-line bending. Stability of the trapped particle mode is
sensitive to the electron connection between the stabilizer and the end plug.
It is found that the stability condition for the trapped particle mode is more
constraining than the stability condition for the MHD mode, and it is
challenging to satisfy the required power constraint. Furthermore a severe
power drain may arise from the necessary connection of low-energy electrons in
the kinetic stabilizer to the central region
Bubble wall perturbations coupled with gravitational waves
We study a coupled system of gravitational waves and a domain wall which is
the boundary of a vacuum bubble in de Sitter spacetime. To treat the system, we
use the metric junction formalism of Israel. We show that the dynamical degree
of the bubble wall is lost and the bubble wall can oscillate only while the
gravitational waves go across it. It means that the gravitational backreaction
on the motion of the bubble wall can not be ignored.Comment: 23 pages with 3 eps figure
Quantum Phase Transitions and the Extended Coupled Cluster Method
We discuss the application of an extended version of the coupled cluster
method to systems exhibiting a quantum phase transition. We use the lattice
O(4) non-linear sigma model in (1+1)- and (3+1)-dimensions as an example. We
show how simple predictions get modified, leading to the absence of a phase
transition in (1+1) dimensions, and strong indications for a phase transition
in (3+1) dimensions
Large N_c, Constituent Quarks, and N, Delta Charge Radii
We show how one may define baryon constituent quarks in a rigorous manner,
given physical assumptions that hold in the large-N_c limit of QCD. This
constituent picture gives rise to an operator expansion that has been used to
study large-N_c baryon observables; here we apply it to the case of charge
radii of the N and Delta states, using minimal dynamical assumptions. For
example, one finds the relation r_p^2 - r_{Delta^+}^2 = r_n^2 - r_{Delta^0}^2
to be broken only by three-body, O(1/N_c^2) effects for any N_c.Comment: 15 pages, 1 eps figure. Version to appear in Phys. Rev.
Isospin splitting in heavy baryons and mesons
A recent general analysis of light-baryon isospin splittings is updated and
extended to charmed baryons.
The measured and splittings stand out as being difficult
to understand in terms of two-body forces alone.
We also discuss heavy-light mesons; though the framework here is necessarily
less general, we nevertheless obtain some predictions that are not strongly
model-dependent.Comment: 12 pages REVTEX 3, plus 4 uuencoded ps figures, CMU-HEP93-
One-loop corrections to the metastable vacuum decay
We evaluate the one-loop prefactor in the false vacuum decay rate in a theory
of a self interacting scalar field in 3+1 dimensions. We use a numerical
method, established some time ago, which is based on a well-known theorem on
functional determinants. The proper handling of zero modes and of
renormalization is discussed. The numerical results in particular show that
quantum corrections become smaller away from the thin-wall case. In the
thin-wall limit the numerical results are found to join into those obtained by
a gradient expansion.Comment: 31 pages, 7 figure
Quantization of Solitons and the Restricted Sine-Gordon Model
We show how to compute form factors, matrix elements of local fields, in the
restricted sine-Gordon model, at the reflectionless points, by quantizing
solitons. We introduce (quantum) separated variables in which the Hamiltonians
are expressed in terms of (quantum) tau-functions. We explicitly describe the
soliton wave functions, and we explain how the restriction is related to an
unusual hermitian structure. We also present a semi-classical analysis which
enlightens the fact that the restricted sine-Gordon model corresponds to an
analytical continuation of the sine-Gordon model, intermediate between
sine-Gordon and KdV.Comment: 29 pages, Latex, minor updatin
Resummation of mass terms in perturbative massless quantum field theory
The neutral massless scalar quantum field in four-dimensional
space-time is considered, which is subject to a simple bilinear
self-interaction. Is is well-known from renormalization theory that adding a
term of the form to the Lagrangean has the formal
effect of shifting the particle mass from the original zero value to m after
resummation of all two-leg insertions in the Feynman graphs appearing in the
perturbative expansion of the S-matrix. However, this resummation is
accompanied by some subtleties if done in a proper mathematical manner.
Although the model seems to be almost trivial, is shows many interesting
features which are useful for the understanding of the convergence behavior of
perturbation theory in general. Some important facts in connection with the
basic principles of quantum field theory and distribution theory are
highlighted, and a remark is made on possible generalizations of the
distribution spaces used in local quantum field theory. A short discussion how
one can view the spontaneous breakdown of gauge symmetry in massive gauge
theories within a massless framework is presented.Comment: 15 pages, LaTeX (style files included), one section adde
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